Kernel smoothing in MATLAB: Theory and practice of kernel smoothing

Kernel Smoothing in MATLAB: Theory and Practice of Kernel Smoothing

Volumn , Issue , 2012, Pages 1-227

  Horová, Ivanka ^a   Koláček, Jan ^a   Zelinka, Jiří ^a  

^a MASARYK UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

BANDWIDTH; DISTRIBUTION FUNCTIONS; STUDENTS; USER INTERFACES;

CUMULATIVE DISTRIBUTION FUNCTION; NON-PARAMETRIC SMOOTHING; OPTIMAL BANDWIDTHS; REGRESSION FUNCTION; SMOOTHING TECHNIQUES; STATISTICAL PROPERTIES; STATISTICAL THEORY; THEORY AND PRACTICE;

MATLAB;

EID: 84995476664     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/8468     Document Type: Book

References (200)

1. Akaike, H. (1970). Statistical predictor information, Annals of the Institute of Statistical Mathematics 22, pp. 203-217.
2. Akaike, H. (1974). Markovian representation of stochastic-processes and its application to analysis of autoregressive moving average processes, Annals of The Institute of Statistical Mathematics 26, 3, pp. 363-387.
3. Altman, N. and Leger, C. (1995). Bandwidth selection for kernel distribution function estimation, Journal of Statistical Planning and Inference 46, pp. 195-214.
4. Anderson, E. (1935). The irises of the Gaspe Peninsula, Bulletin of the American Iris Society 59, pp. 2-5.
5. Anderson, R. (2007). The credit scoring toolkit: theory and practice for retail credit risk management and decision automation (Oxford University Press).
6. Azzalini, A. (1981). A note on the estimation of a distribution function and quantiles by a kernel method, Biometrika 68, 1, pp. 326-328.
7. Bowman, A. (1984). An alternative method of cross-validation for the smoothing of density estimates, Biometrika 71, 2, pp. 353-360.
8. Bowman, A., Hall, P. and Prvan, T. (1998). Bandwidth selection for the smoothing of distribution functions, Biometrika 85, 4, pp. 799-808.
9. Bowman, A. W. and Azzalini, A. (1997). Applied smoothing techniques for data analysis: The kernel approach with S-plus illustrations, Oxford statistical science series (Oxford University Press, USA).
10. Brillinger, D. (2001). Time series: data analysis and theory, Classics in applied mathematics (Society for Industrial and Applied Mathematics).
11. Cao, R., Cuevas, A. and González Manteiga, W. (1994). A comparative study of several smoothing methods in density estimation, Computational Statistics and Data Analysis 17, 2, pp. 153-176.
12. Chacón, J. E. and Duong, T. (2010). Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices, Test 19, 2, pp. 375-398.
13. Chacón, J. E. and Duong, T. (2012). Bandwidth selection for multivariate density derivative estimation, with applications to clustering and bump hunting, ArXiv e-prints URL http://adsabs.harvard.edu/abs/2012arXiv1204. 6160C.
14. Chacón, J. E., Duong, T. and Wand, M. P. (2011). Asymptotics for general multivariate kernel density derivative estimators, Statistica Sinica 21, 2, pp. 807-840.
15. Chaudhuri, P. and Marron, J. S. (1999). SiZer for exploration of structures in curves, Journal of the American Statistical Association 94, 447, pp. 807-823.
16. Cheng, M.-Y. (1997). Boundary aware estimators of integrated density derivative products, Journal of the Royal Statistical Society. Series B (Methodological)59, 1, pp. 191-203.
17. Chiu, S. (1990). Why bandwidth selectors tend to choose smaller bandwidths, and a remedy, Biometrika 77, 1, pp. 222-226.
18. Chiu, S. (1991). Some stabilized bandwidth selectors for nonparametric regression, Annals of Statistics 19, 3, pp. 1528-1546.
19. Chu, C. K. and Marron, J. S. (1991). Choosing a kernel regression estimator, Statistical Science 6, 4, pp. 404-419.
20. Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scat- terplots, Journal of the American Statistical Association 74, 368, pp. 829-836.
21. Cline, D. and Hart, J. (1991). Kernel estimation of densities of discontinuous derivatives, Statistics 22, pp. 69-84.
22. Collet, D. (1997). Modelling survival data in medical research (Chapman & Hall/CRC, Boca Raton, London, New York, Washington D.C.).
23. Coppock, D. S. (2002). Why lift? www.dmreview.com/news/5329-1.html.
24. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions - estimating the correct degree of smoothing by the method of generalized cross-validation, Numerische Mathematik 31, 4, pp. 377-403.
25. Deheuvels, P. (1977). Estimation nonparametrique de la densité par histogrammes generalisés, Rev. Statist. Appl. 35, pp. 5-42.
26. DeLong, E., DeLong, D. and D.L. Clarke-Pearson, D. L. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach, Biometrics 44, 3, pp. 837-845.
27. Devroye, L. and Lugosi, G. (1997). Nonasymptotic universal smoothing factors, kernel complexity and Yatracos classes, The Annals of Statistics 25, 6, pp. 2626-2637.
28. Doleželová, H., Šlampa, P., Ondrová, B., Gombošová, A., Šovadinová, Š., Novotný, T., Bolčák, K., Růžičková, J., Hynková, L. and Forbelská, M. (2008). The impact of PET with 18FDG in radiotherapy treatment planning and in the prediction in patients with cervix carcinoma - results of pilot study, Neoplasma 55, 5, pp. 437-441.
29. Doubek, M., Jungová, A., Brejcha, M., Panovská, A., Brychtova, Y., Posplsil, Z. and Mayer, J. (2009). Alemtuzumab in chronic lymphocytic leukemia treatment: retrospective analysis of outcome according to cytogenetics, Vnitrm lékařství (Internal Medicine, in Czech) 55, 6, pp. 549-554.
30. Droge, B. (1996). Some comments on cross-validation, Tech. Rep. 1994-7, Humboldt Universitaet Berlin, URL http://ideas.repec.org/p/wop/humbsf/ 1994-7.html.
31. Duong, T. (2004). Bandwidth selectors for multivariate kernel density estimation, Ph.D. thesis, School of Mathematics and Statistics, University of Western Australia.
32. Duong, T. (2007). ks: Kernel density estimation and kernel discriminant analysis for multivariate data in R, Journal of Statistical Software 21, 7, pp. 1-16.
33. Duong, T., Cowling, A., Koch, I. and Wand, M. P. (2008). Feature significance for multivariate kernel density estimation, Computational Statistics & Data Analysis 52, 9, pp. 4225-4242.
34. Duong, T. and Hazelton, M. (2005a). Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation, Journal of Multivariate Analysis 93, 2, pp. 417-433.
35. Duong, T. and Hazelton, M. (2005b). Cross-validation bandwidth matrices for multivariate kernel density estimation, Scandinavian Journal of Statistics32, 3, pp. 485-506.
36. Engel, E. (1857). Die Productions und Consumtionsverhaltnisse des Konigreichs Sachsen, Zeitschrift des statistischen Bureaus des Koniglich Sachsischen Ministerium des Inneren 8,9.
37. Epanechnikov, V. A. (1969). Non-parametric estimation of a multivariate probability density, Theory of Probability and its Applications 14, 1, pp. 153-158.
38. Eubank, R. (1988). Spline smoothing and nonparametric regression, 1st edn. (Dekker, New York).
39. Fan, J. (1992). Design-adaptive nonparametric regression, Journal of the American Statistical Association 87, 420, pp. 998-1004.
40. Fan, J. and Gijbels, I. (1995). Data-driven bandwidth selection in local polynomial fitting: Variable bandwidth and spatial adaptation, Journal of the Royal Statistical Society. Series B (Methodological) 57, 2, pp. pp. 371-394.
41. Fang, K., Kotz, S. and Ng, K. (1990). Symmetric multivariate and related distributions (Chapman and Hall, London; New York).
42. Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics, Philosophical Transactions of the Royal Society of London, A 222, pp. 309-368.
43. Fisher, R. A. (1932). Statistical methods for research workers (Oliver & Boyd, Edinburgh).
44. Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems, Annals of Human Genetics 7, 2, pp. 179-188.
45. Forbelska, M. (2007). Elliptically contoured models in ROC analysis, in S.Co.2007, Fifth Conference, Book of Short Papers, pp. 243-248.
46. Gasser, T. and Müller, H.-G. (1979). Kernel estimation of regression functions, in T. Gasser and M. Rosenblatt (eds.), Smoothing Techniques for Curve Estimation, Lecture Notes in Mathematics, Vol. 757 (Springer Berlin/Heidelberg), pp. 23-68.
47. Gasser, T., Müller, H.-G. and Mammitzsch, V. (1985). Kernels for nonparametric curve estimation, Journal of the Royal Statistical Society. Series B (Methodological) 47, 2, pp. 238-252.
48. Godtliebsen, F., Marron, J. S. and Chaudhuri, P. (2002). Significance in scale space for bivariate density estimation, Journal of Computational and Graphical Statistics 11, 1, pp. 1-21.
49. Gonzalez-Manteiga, W., Cao, R. and Marron, J. S. (1996). Bootstrap selection of the smoothing parameter in nonparametric hazard rate estimation, Journal of the American Statistical Association 91, 435, pp. 1130-1140.
50. Granovsky, B. and Müller, H.-G. (1989). On the optimality of a class of polynomial kernel functions, Journal of Statistics and Decisions 7, pp. 301-312.
51. Granovsky, B. and Müller, H.-G. (1991). Optimizing kernel methods - a unifying variational principle, International Statistical Review 59, 3, pp. 373-388.
52. Granovsky, B. L., Müller, H.-G. and Pfeifer, C. (1995). Some remarks on optimal kernel functions, Journal of Statistics and Decisions 13, 2, pp. 101-116.
53. Graunt, J. (1662). Natural and political observations made upon the bills of mortality (Martyn London).
54. Hall, P. and Marron, J. S. (1987). On the amount of noise inherent in bandwidth selection for a kernel density estimator, The Annals of Statistics 15, 1, pp. 163-181.
55. Hall, P. and Park, B. U. (2002). New methods for bias correction at endpoints and boundaries, The Annals of Statistics 30, 5, pp. 1460-1479.
56. Hall, P. and Wehrly, T. E. (1991). A geometrical method for removing edge effects from kernel-type nonparametric regression estimators, Journal of the American Statistical Association 86, 415, pp. pp. 665-672.
57. Hand, D. and Henley, W. (1997). Statistical classification methods in consumer credit scoring: a review, Journal of the Royal Statistical Society, Series A. 160, 3, pp. 523-541.
58. Härdle, W. (1990). Applied Nonparametric Regression, 1st edn. (Cambridge University Press, Cambridge).
59. Härdle, W., Hall, P. and Marron, J. (1988). How far are automatically chosen regression smoothing parameters from their optimum, Journal of the American Statistical Association 83, 401, pp. 86-95.
60. Härdle, W., Marron, J. S. and Wand, M. P. (1990). Bandwidth choice for density derivatives, Journal of the Royal Statistical Society. Series B (Methodological) 52, 1, pp. 223-232.
61. Härdle, W., Müller, M., Sperlich, S. and Wewatz, A. (2004). Nonparametric and, Semiparametric Models, 1st edn. (Heidelberg: Springer).
62. Hjort, N. and Jones, M. (1996). Locally parametric nonparametric density estimation, The Annals of Statistics 24, 4, pp. 1619-1647.
63. Horová, I. (1996). Gegenbauer polynomials, optimal kernels and Stancu operators, in Approximation Theory and Function Series (Budapest: Janos Bolyai Mathematical Society), pp. 227-235.
64. Horová, I. (1997). Boundary kernels, in Summer schools MATLAB 94,95 (Brno: Masaryk University), pp. 17-24.
65. Horová, I. (2000). Some remarks on kernels, Journal of Computational Analysis and Applications 2, pp. 253-263.
66. Horová, I. (2002). Optimization problems connected with kernel estimates, Electrical and Computer Engineering Series (WSEAS Press), pp. 334-339.
67. Horová, I., Koláček, J. and Vopatová, K. (2009). Bandwidth matrix choice for bivariate kernel density estimates, in Book of short papers (MU Brno), pp.
68. Horová, I., Koláček, J. and Vopatová, K. (2012a). Full bandwidth matrix selectors for gradient kernel density estimate, Computational Statistics & Data Analysis, submitted.
69. Horová, I., Koláček, J. and Vopatová, K. (2012b). Visualization and bandwidth matrix choice, Communications in Statistics - Theory and Methods 41, 4, pp. 759-777.
70. Horová, I., Koláček, J., Zelinka, J. and El-Shaarawi, A. H. (2008a). Smooth estimates of distribution functions with application in environmental studies, in Advanced topics on mathematical biology and ecology (WSEAS Press), pp. 122-127.
71. Horová, I., Koláček, J., Zelinka, J. and Vopatová, K. (2008b). Bandwidth choice for kernel density estimates, in Proceedings IASC, Yokohama: IASC, 2008, pp. 542-551.
72. Horová, I., Pospíšil, Z. and Zelinka, J. (2007). Semiparametric estimation of hazard function for cancer patients, Sankhya: The Indian Journal of Statistics69, 3, pp. 494-513.
73. Horová, I., Pospíšil, Z. and Zelinka, J. (2009). Hazard function for cancer patients and cancer cell dynamics, Journal of Theoretical Biology 258, 3, pp. 437-443.
74. Horová, I., Vieu, P. and Zelinka, J. (2002). Optimal choice of nonparametric estimates of a density and of its derivatives, Statistics & Decisions 20, 4, pp. 355-378.
75. Horováa, I. and Vopatová, K. (2011). Kernel gradient estimate, in F. Ferraty (ed.), Recent Advances in Functional Data Analysis and Related Topics (Springer- Verlag Berlin Heidelberg), pp. 177-182.
76. Horová, I. and Zelinka, J. (2007a). Contribution to the bandwidth choice for kernel density estimates, Computational Statistics 22, 1, pp. 31-47.
77. Horová, I. and Zelinka, J. (2007b). Kernel estimation of hazard functions for biomedical data sets, in W. Härdle, Y. Mori and P. Vieu (eds.), Statistical Methods for Biostatistics and Related Fields, Mathematics and Statistics (Springer-Verlag Berlin Heidelberg), pp. 64-86.
78. Horová, I., Zelinka, J. and Budíková, M. (2006). Kernel estimates of hazard functions for carcinoma data sets, Environmetrics 17, 3, pp. 239-255.
79. Hougaard, P. (2001). Analysis of Multivariate Survival Data (Springer-Verlag, New York, Berlin, Heidelberg).
80. Hurt, J. (1992). Statistical methods for survival data analysis, in Proceedings ROBUST’92, Eds. J.Antoch & G.Dohnal, pp. 54-74.
81. Jiang, J. and Marron, J. S. (2003). Sizer for censored density and hazard estimation, Preprint.
82. Jones, M. and Sheather, S. (1991). Using nonstochastic terms to advantage in kernel-based estimation of integrated squared density derivatives, Statistics & Probability Letters 11,6, pp. 511-514.
83. Jones, M. C. (1993). Simple boundary correction for kernel density estimation, Statistics and Computing 3, pp. 135-146.
84. Jones, M. C. and Kappenman, R. F. (1991). On a class of kernel density estimate bandwidth selectors, Scandinavian Journal of Statistics 19, 4, pp. 337-349.
85. Jones, M. C., Marron, J. S. and Park, B. U. (1991). A simple root n bandwidth selector, The Annals of Statistics 19, 4, pp. 1919-1932.
86. Kaplan, E. I. and Meier, P. V. (1958). Nonparametric estimation from incomplete observations, Journal of the American Statistical Association 53, 282, pp. 457-481.
87. Karunamuni, R. and Alberts, T. (2005a). On boundary correction in kernel density estimation, Statistical Methodology 2, pp. 191-212.
88. Karunamuni, R. and Alberts, T. (2005b). A generalized reflection method of boundary correction in kernel density estimation, Canad. J. Statist. 33, pp. 497-509.
89. Karunamuni, R. and Alberts, T. (2006). A locally adaptive transformation method of boundary correction in kernel density estimation, J. Statist. Planning and Inference 136, pp. 2936-2960.
90. Karunamuni, R. and Zhang, S. (2008). Some improvements on a boundary corrected kernel density estimator, Statistics & Probability Letters 78, pp. 497-507.
91. Kim, C., Bae, W., Choi, H. and Park, B. U. (2005). Non-parametric hazard function estimation using the Kaplan-Meier estimator, Journal of Non- parametric Statistics 17, 8, pp. 937-948.
92. Klein, J. and Moeschberger, M. (2003). Survival analysis: techniques for censored, and truncated data, Statistics for biology and health (Springer).
93. Koláček, J. (2002). Kernel estimation of the regression function - bandwidth selection, in Summer School DATASTAT01 Proceedings FOLIA (MU Brno), pp. 129-138.
94. Koláček, J. (2005). Kernel Estimation of the Regression Function (in Czech), Ph.D. thesis, Masaryk University, Brno.
95. Koláček, J. (2008). An improved estimator for removing boundary bias in kernel cumulative distribution function estimation (in Czech), in Proceedings in Computational Statistics C0MPSTAT’08, pp. 549-556.
96. Koláček, J. (2008). Plug-in method for nonparametric regression, Computational Statistics 23, 1, pp. 63-78.
97. Koláček, J. and Karunamuni, R. J. (2009). On boundary correction in kernel estimation of ROC curves, Austrian Journal of Statistics 38, 1, pp. 17-32.
98. Koláček, J. and Karunamuni, R. J. (2011). A generalized reflection method for kernel distribution and hazard functions estimation, Journal of Applied Probability and Statistics 6, 2, pp. 73-85.
99. Koláček, J. and Poměnková, J. (2006). A comparative study of boundary effects for kernel smoothing, Austrian Journal of Statistics 35, 2, pp. 281-289.
100. Koláček, J. and Řezáč, M. (2010). Assessment of scoring models using information value, in 19th International Conference on Computational Statistics, Paris France, August 22-27, 2010 Keynote, Invited and Contributed Papers, pp. 1191-1198.
101. Koláček, J. and Řezáč, M. (2011). Quality measures for predictive scoring models, in Proceedings ASMDA 2011 (Roma, Italy), pp. 720-727.
102. Koláček, J. and Zelinka, J. (2012). MATLAB toolbox, URL http://www.math.muni.cz/english/science-and-research/developed-software/ 232-matlab-toolbox.html.
103. Koziol, J. A. and Green, S. B. (1976). Cramer-von Mises statistic for randomly censored data, Biometrika 63, 3, pp. 465-474.
104. Kozusko, F. and Bajzer, Z. (2003). Combining gompertzian growth and cell population dynamics, Mathematical Biosciences 185, 2, pp. 153-167.
105. Krzanowski, W. J. and Hand, D. J. (2009). ROC curves for continuous data, Monographs on statistics and applied probability (CRC Press).
106. Kullback, S. and Leibler, R. A. (1951). On information and sufficiency, The Annals of Mathematical Statistics 22, 1, pp. 79-86.
107. Lejeune, M. (1985). Estimation non-parametrique par noyaux: regression poly- nomiale mobile, Revue de Statistique Applique 33, 3, pp. 43-67.
108. Lejeune, M. and Sarda, P. (1992). Smooth estimators of distribution and density functions, Computational Statistics & Data Analysis 14, pp. 457-471.
109. Li, K.-C. (1985). From Stein’s unbiased risk estimates to the method of generalized cross validation, The Annals of Statistics 13, 4, pp. 1352-1377.
110. Lloyd, C. (1998). Using smoothed receiver operating characteristic curves to summarize and compare diagnostic systems, Journal of the American Statistical Association 93, 444.
111. Lloyd, C. (2002). Estimation of a convex ROC curve, Statistics & Probability Letters 59, 1, pp. 99-111.
112. Lloyd, C. and Yong, Z. (1999). Kernel estimators of the ROC curve are better than empirical, Statistics & Probability Letters 44, pp. 221-228.
113. Loader, C. R. (1996). Local likelihood density estimation, The Annals of Statistics24, 4, pp. 1602-1618.
114. Lusted, L. B. (1971). Signal detectability and medical decision-making, Science171, 3977, pp. 1217-1219, doi:10.1126/science.171.3977.1217, URL http://www.sciencemag.org/content/171/3977/1217.short.
115. Mack, Y. P. and Müller, H.-G. (1988). Convolution type estimators for nonpara- metric regression, Statistics & Probability Letters 7, 3, pp. 229-239.
116. Magnus, J. R. and Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics, 2nd edn. (John Wiley & Sons).
117. Mallows, C. (1973). Some comments on Cp, Technometrics 15, 4, pp. 661-675.
118. Mammitzsch, V. (1985). The fluctuation of kernel estimators under certain moment conditions, in Proc. ISI (ISI’85), pp. 17-18.
119. Marron, J. S. (1996). A personal view of smoothing and statistics, in W. Härdle and M. Schimek (eds.), Statistical Theory and Computational Aspects of Smoothing, Contributions to Statistics (Physica-Verlag), pp. 1-9.
120. Marron, J. S. and Nolan, D. (1988). Canonical kernels for density-estimation, Statistics & Probability Letters 7, 3, pp. 195-199.
121. Marron, J. S. and Padgett, W. J. (1987). Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples, Annals of Statistics 15, 4, pp. 1520-1535.
122. Marron, J. S. and Ruppert, D. (1994). Transformations to reduce boundary bias in kernel density estimation, Journal of the Royal Statistical Society. Series B (Methodological) 56, 4, pp. 653-671.
123. Mielniczuk, J. (1986). Some asymptotic properties of kernel estimators of a density function in case of censored data, Annals of Statistics 14, 2, pp. 766-773.
124. Minnotte, M. C. (1993). A test of mode existence with application to multimodality, Ph.D. thesis, Rice University, TX, USA.
125. Müller, H., StadtMüller, U. and Schmitt, T. (1987). Bandwidth choice and confidence-intervals for derivatives of noisy data, Biometrika 74, 4, pp. 743-749.
126. Müller, H.-G. (1987). Weighted local regression and kernel methods for nonpara- metric curve fitting, Journal of the American Statistical Association 82, 397, pp. 231-238.
127. Müller, H.-G. (1988). Nonparametric regression analysis of longitudinal data(Springer, New York).
128. Müller, H.-G. (1991). Smooth optimum kernel estimators near endpoints, Biometrika 78, 3, pp. 521-530.
129. Müller, H. G. and Wang, J. L. (1990a). Locally adaptive hazard smoothing, Probability Theory and Related Fields 85, 4, pp. 523-538.
130. Müller, H. G. and Wang, J. L. (1990b). Nonparametric analysis of changes in hazard rates for censored survival data - an alternative to change-point models, Biometrika 77, 2, pp. 305-314.
131. Müller, H. G. and Wang, J. L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths, Biometrics 50, 1, pp. 6176.
132. Nadaraya, E. A. (1964). On estimating regression, Theory of Probability and its Applications 9, 1, pp. 141-142.
133. Nelson, W. (1972). Theory and applications of hazard plotting for censored data, Technometrics 14, pp. 945-966.
134. Nielsen, J. P. and Linton, O. B. (1995). Kernel estimation in a nonparametric marker dependent hazard model, Annals of Statistics 23, 5, pp. 1735-1748.
135. Nováková, J. (2009). Kernel cumulative distribution function estimates (in Czech), Master’s thesis, Masaryk University, Brno.
136. Parzen, E. (1962). On estimation of a probability density function and mode, The Annals of Mathematical Statistics 33, 3, pp. 1065-1076.
137. Patil, P. N. (1993a). Bandwidth choice for nonparametric hazard rate estimation, Journal of Statistical Planning and Inference 35, 1, pp. 15-30.
138. Patil, P. N. (1993b). On the least-squares cross-validation bandwidth in hazard rate estimation, Annals of Statistics 21, 4, pp. 1792-1810.
139. Patil, P. N., Wells, M. T. and Marron, J. S. (1994). Some heuristics of kernel based estimators of ratio functions, Nonparametrics Statistics 4, pp. 283-289.
140. Pepe, M. (2004). The statistical evaluation of medical tests for classification and, prediction, Oxford statistical science series (Oxford University Press).
141. Priestley, M. B. and Chao, M. T. (1972). Non-parametric function fitting, Journal of the Royal Statistical Society. Series B (Methodological) 34, 3, pp. 385-392.
142. Ramlau-Hansen, C. H. (1983). Counting processes intensities by means of kernel functions, The Annals of Statistics 11, 2, pp. 453-466.
143. Reiss, R.-D. (1981). Nonparametric estimation of smooth distribution functions, Scand. J. Stat., Theory Appl. 8, pp. 116-119.
144. Ren, H., X.H. Zhou and Liang, H. (2004). A flexible method for estimating the ROC curve, Journal of Applied Statistics 31, 7, pp. 773-784.
145. Řezáč, F. and Řezáč, M. (2011). How to measure the quality of credit scoring models, Czech Journal of Economics and Finance 61, 5, pp. 486-507.
146. Řezáč, M. (2007). Kernel density estimates (in Czech), Ph.D. thesis, Masaryk University, Brno.
147. Řezáč, M. and Koláček, J. (2010). On aspects of quality indexes for scoring models, in 19th International Conference on Computational Statistics, Paris France, August 22-27, 2010 Keynote, Invited and Contributed Papers, pp. 1517-1524.
148. Řezáč, M. and Koláček, J. (2011). Adjusted empirical estimate of information value for credit scoring models, in Proceedings ASMDA 2011 (Roma, Italy), pp. 1162-1169.
149. Rice, J. (1984). Bandwidth choice for nonparametric regression, Annals of Statistics 12, 4, pp. 1215-1230.
150. Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function, The Annals of Mathematical Statistics 27, 3, pp. 832-837.
151. Sain, S., Baggerly, K. and Scott, D. (1994). Cross-validation of multivariate densities, Journal of the American Statistical Association 89, 427, pp. 807-817.
152. Sarda, P. (1993). Smoothing parameter selection for smooth distribution functions, Journal of Statistical Planning and Inference 35, pp. 65-75.
153. Sarda, P. and Vieu, P. (1991). Smoothing parameter selection in hazard estimation, Statistics & Probability Letters 11, 5, pp. 429-434.
154. Scheffé, H. (1959). The analysis of variance, Wiley Classics Library (Wiley- Interscience Publication).
155. Schuster, E. (1985). Incorporating support constraints into nonparametric estimators of densities, Communications in Statistics-Theory end Methods 14, 5, pp. 1123-1136.
156. Scott, D. W. (1992). Multivariate density estimation: theory, practice, and visualization (Wiley).
157. Scott, D. W. and Terrell, G. R. (1987). Biased and unbiased cross-validation in density estimation, Journal of the American Statistical Association 82, 400, pp. 1131-1146.
158. Searle, S. (1987). Linear models for unbalanced data (Wiley).
159. Seber, G. (1977). Linear regression analysis (Wiley).
160. Seifert, B. and Gasser, T. (1996). Variance properties of local polynomials and ensuing modifications, in W. Härdle and M. Schimek (eds.), Statistical Theory and Computational Aspects of Smoothing, Contributions to Statistics (Physica-Verlag), pp. 50-79.
161. Shibata, R. (1981). An optimal selection of regression variables, Biometrika 68, pp. 45-54.
162. Siddiqi, N. (2006). Credit risk scorecards: developing and implementing intelligent credit scoring, Wiley and SAS Business Series (Wiley).
163. Silverman, B. W. (1985). Some aspects of the spline smoothing approach to nonparametric regression curve fitting, Journal of the Royal Statistical Society. Series B (Methodological) 47, pp. 1-52.
164. Silverman, B. W. (1986). Density estimation for statistics and data analysis(Chapman and Hall, London).
165. Simonoff, J. S. (1996). Smoothing Methods in Statistics (Springer-Verlag, New York).
166. Soumarova, R., Horová, H., Ruzickova, J., Coupek, P., Slampa, P., Seneklova, Z., Petrakova, K., Budlkova, M. and Horová, I. (2002). Local and distant failure in patients with stage i and ii carcinoma of the breast treated with breat-conserving surgery and radiation therapy (in Czech, English summary), Radiacm onkologie 2, 1, pp. 17-24.
167. Stoer, J. and Bulirsch, R. (2002). Introduction to numerical analysis, 3rd edn., Texts in applied mathematics (Springer).
168. Stone, C. J. (1977). Consistent nonparametric regression, The Annals of Statistics5, 4, pp. 595-620.
169. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions, Journal of the Royal Statistical Society Series B-Statistical Methodology 36, 2, pp. 111-147.
170. Sturges, H. A. (1926). The choice of a class interval, Journal of the American Statistical Association 21, 153, pp. pp. 65-66.
171. Szegő, G. (1939). Orthogonal polynomials (American Mathematical Society, Providence).
172. Tanner, M. A. and Wong, W. H. (1983). The estimation of the hazard function from randomly censored data by the kernel method, Annals of Statistics3, pp. 989-993.
173. Tanner, M. A. and Wong, W. H. (1984). Data-based nonparametric estimation of the hazard function with applications to model diagnostics and exploratory analysis, Journal of the American Statistical Association 79, 385, pp. 174-182.
174. Terrell, G. R. (1990). The maximal smoothing principle in density estimation, Journal of the American Statistical Association 85, 410, pp. 470-477.
175. Terrell, G. R. and Scott, D. W. (1985). Oversmoothed nonparametric density estimates, Journal of the American Statistical Association 80, 389, pp. 209-214.
176. Thernau, T. M. and Grambsch, P. M. (2001). Modelling survival data. extending the Cox model (Springer-Verlag, New York, Berlin, Heidelberg).
177. Thomas, L. (2009). Consumer credit models: pricing, profit, and portfolios (Oxford University Press).
178. Tukey, J. W. (1961). Curves as parameters, and touch estimation, in Proceedings of the 4th Symposium on Mathematics, Statistics and Probability, pp. 681-694.
179. Tukey, J. W. (1977). Exploratory data analysis (Addison-Wesley).
180. UNICEF (2003). The state of the worlds children 2003, http://www.unicef.org/ sowc03/index.html.
181. Uzunogullari, U. and Wang, J. L. (1992). A comparison of hazard rate estimators for left truncated and right censored data, Biometrika 79, 2, pp. 297-310.
182. Vopatová, K. (2012). K-web: KDE, http://k101.unob.cz/~Vopatova/kde.htm.
183. Vopatová, K., Horová, I. and Koláček, J. (2010). Bandwidth choice for kernel density derivative, in Proceedings of the 25th International Workshop on Statistical Modelling (Glasgow, Scotland), pp. 561-564.
184. Wan, S. and Zhang, B. (2008). Comparing correlated ROC curves for continuous diagnostic tests under density ratio models, Computational Statistics & Data Analysis 53, 1, pp. 233-245.
185. Wand, M. and Jones, M. (1993). Comparison of smoothing parameterizations in bivariate kernel density-estimation, Journal of The American Statistical Association 88, 422, pp. 520-528.
186. Wand, M. and Jones, M. (1995). Kernel smoothing (Chapman and Hall, London).
187. Wand, M. P. and Jones, M. C. (1994). Multivariate plug-in bandwidth selection, Computational Statistics 9, 2, pp. 97-116.
188. Watson, G. S. (1964). Smooth regression analysis, Sankhya: The Indian Journal of Statistics, Series A 26, 4, pp. 359-372.
189. Watson, G. S. and Leadbetter, M. R. (1964). Hazard analysis I, Biometrika 51, 1/2, pp. 175-184.
190. Whittle, P. (1958). On the smoothing of probability density functions, Journal of the Royal Statistical Society. Series B 55, pp. 549-557.
191. Xu, K. (2003). How has the literature on Gini’s index evolved in the past 80 years? SSRN eLibrary.
192. Yandell, B. (1983). Nonparametric inference for rates with censored survival data, Annals of Statistics 11, 4, pp. 1119-1135.
193. Youndjé, E., Sarda, P. and Vieu, P. (1996). Optimal smooth hazard estimates, Test 5, 2, pp. 379-394.
194. Zelinka, J. and Horováa, I. (2001). Kernel estimates of a derivative of a regession function (in Czech), in Proceedings ROBUST 2000, Eds. J.Antoch, pp. 382-391.
195. Zhang, S. and Karunamuni, R. (1998). On kernel density estimation near endpoints, Journal of Statistical Planning and Inference 70, pp. 301-316.
196. Zhang, S. and Karunamuni, R. (2000). On nonparametric density estimation at the boundary, Journal Of Nonparametric Statistics 12, 2, pp. 197-221.
197. Zhang, S., Karunamuni, R. J. and Jones, M. C. (1999). An improved estimator of the density function at the boundary, Journal of the American Statistical Association 94, 448, pp. 1231-1241.
198. Zhou, X. and Harezlak, J. (2002). Comparison of bandwidth selection methods for kernel smoothing of ROC curves, Statistics in Medicine 21, 14, pp. 2045-2055.
199. Zhou, X., Obuchowski, N. and McClish, D. (2002). Statistical methods in diagnostic medicine, 1 (Wiley-Interscience).
200. Zou, K., Hall, W. and Shapiro, D. (1997). Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests, Statistics in Medicine 16, 19, pp. 2143-2156.