Some automated methods of smoothing time-dependent data

Journal of Nonparametric Statistics

Volumn 6, Issue 2-3, 1996, Pages 115-142

  Hart, Jeffrey D ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Autoregression; Blockwise cross validation; Cross validation; Kernel estimators; Mean integrated squared error; Plug in rules; Prequential analysis; Time series cross validation; Transition densities

Indexed keywords

EID: 3042990270     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259608832667     Document Type: Article

References (87)

1. Ahmad, I. A. (1977). Strong consistency of density estimation by orthogonal series methods for dependent variables with applications. Annals of the Institute of Statistical Mathematics 31, 279-288.
2. Altman, N. S. (1990). Kernel smoothing of data with correlated errors. Journal of the American Statistical Association 85, 749-759.
3. Baek, J. and Wehrly, T. E. (1993). Kernel estimation for additive models under dependence. Stochastic Processes and their Applications 47, 95-112.
4. Banon, G. (1977). Estimation nonparamétrique de densite de probabilite pour les processus de Markov. Thèse, Universite Paul Sabatier de Toulouse, France.
5. Bierens, H. J. (1983). Uniform consistency of kernel estimators of a regression function under generalized conditions. Journal of the American Statistical Association 78, 699-707.
6. Boularan, J., Ferré, L. and Vieu, P. (1994). Growth curves: a two-stage nonparametric approach. Journal of Statistical Planning and Inference 38, 327-350.
7. Bowman, A. W. (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika 71, 353-360.
8. Buja, A., Hastie, T. and Tibshirani, R. (1989). Linear smoothers and additive models (with discussion). Annals of Statistics 17, 453-555.
9. Castellana, J. V. and Leadbetter, M. R. (1986). On smoothed probability density estimation for stationary processes. Stochastic Processes and their Applications 21, 179-193.
10. Chanda, K. C. (1983). Density estimation for linear processes. Annals of the Institute of Statistical Mathematics 35, 439-446.
11. Chiu, S.-T. (1989). Bandwidth selection for kernel estimate with correlated noise. Statistics and Probability Letters 8, 347-354.
12. Chu, C. K. and Marron, J. S. (1991). Comparison of two bandwidth selectors with dependent errors. Annals of Statistics 19, 1906-1918.
13. Chui, C. K. (1992). An Introduction to Wavelets. Academic Press, San Diego, CA.
14. Collomb, G. (1984). Propriétés de convergence presque complète du prédicteur à noyau. Zeit. Wahr. ver. Geb. 66, 441-460.
15. Dawid, A. P. (1984). Statistical theory: the prequential approach (with discussion). Journal of the Royal Statistical Society A 147, 278-292.
16. Delecroix, M. (1975). Sur l'estimation des densites marginales et de transition d'un processus stationaire at melangeant. Ph.D. Thesis, University of Sciences and Techniques of Lille, France.
17. Diggle, P. (1990). Time Series, A Biostatistical Introduction. Clarendon, Oxford.
18. Efron, B. and Morris, C. N. (1973). Stein's estimation rule and its competitors - An empirical Bayes approach, Journal of the American Statistical Association 68, 117-130.
19. Eubank, R. L. and Hart, J. D. (1992). Testing goodness-of-fit in regression via order selection criteria. Annals of Statistics 20, 1412-1425.
20. Eubank, R. L. and Speckman, P. L. (1993). Confidence bands in nonparametric regression. Journal of the American Statistical Association 88, 1287-1301.
21. Fan, J. (1992). Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 998-1004.
22. Fraiman, R. and Meloche, J. (1994). Smoothing dependent observations. Statistics and Probability Letters, to appear.
23. Gasser, T. and Müller, H.-G. (1979). Kernel estimation of regression functions. In Smoothing Techniques for Curve Estimation (eds. Th. Gasser and M. Rosenblatt) 23-68. Springer, Berlin (Lecture Notes in Mathematics No. 757).
24. Gasser, T., Müller, H.-G., Köhler, W., Molinari, L. and Prader, A. (1984). Nonparametric analysis of growth curves. Annals of Statistics 12, 210-229.
25. Györfi, L., Härdle, W., Sarda, P. and Vieu, P. (1990). Nonparametric Curve Estimation from Time Series. Lecture Notes in Statistics 60. Springer-Verlag, Heidelberg.
26. 2 strong consistency of recursive density estimation from dependent samples. IEEE Transactions on Information Theory 36, 531-539.
27. Hall, P. (1983). Large sample optimality of least squares cross-validation in density estimation. Annals of Statistics 11, 1156-1174.
28. Hall, P. and Hart, J. D. (1990a). Convergence rates in density estimation for data from infinite-order moving average processes. Probability Theory and Related Fields 87, 253-274.
29. Hall, P. and Hart, J. D. (1990b). Bootstrap test for difference between means in nonparametric regression. Journal of the American Statistical Association 85, 1039-1049.
30. Hall, P. and Hart, J. D. (1990c). Nonparametric regression with long-range dependence. Stochastic Processes and their Applications 36, 339-351.
31. Hall, P. and Heyde, C. (1980). Martingale Limit Theory and Its Applications. Academic Press, New York.
32. Hall, P. and Johnstone, I. (1992). Empirical functionals and efficient smoothing parameter selection (with discussion). Journal of the Royal Statistical Society B 54, 475-530.
33. Hall, P., Lahiri, S. N. and Truong, Y. K. (1994). On bandwidth choice for density estimation with dependent data. Manuscript.
34. Hall, P., Sheather, S. J., Jones, M. C. and Marron, J. S. (1991). On optimal data-based bandwidth selection in kernel density estimation. Biometrika 78, 263-269.
35. Härdle, W., Hall, P. and Marron, J. S. (1988). How far are automatically chosen regresssion smoothing parameters from their optimum? (with discussion) Journal of the American Statistical Association 83, 86-99.
36. Härdle, W. and Vieu, P. (1992). Kernel regression smoothing of time series. Journal of Time Series Analysis 13, 209-232.
37. Hart, J. D. (1984). Efficiency of a kernel density estimator under an autoregressive dependence model. Journal of the American Statistical Association 79, 110-117.
38. Hart, J. D. (1989). Kernel smoothing when the observations are correlated. Technical Report # 35, Department of Statistics, Texas A & M University.
39. Hart, J. D. (1991). Kernel regression estimation with time series errors. Journal of the Royal Statistical Society B 53, 173-187.
40. Hart, J. D. (1994). Automated kernel smoothing of dependent data by using time series cross-validation. Journal of the Royal Statistical Society, Series B 56, 529-542.
41. Hart, J. D. and Vieu, P. (1990). Data-driven bandwidth choice for density estimation based on dependent data. Annals of Statistics 18, 873-890.
42. Hart, J. D. and Wehrly, T. E. (1986). Kernel regression estimation using repeated measurements data. Journal of the American Statistical Association 81, 1080-1088.
43. Hart, J. D. and Wehrly, T E., (1992). Kernel regression when the boundary region is large, with an application to testing the adequacy of polynomial models. Journal of the American Statistical Association 87, 1018-1024.
44. Hart, J. D. and Wehrly, T. E. (1993). Consistency of cross-validation when the data are curves. Stochastic Processes and their Applications 45, 351-361.
45. Hastie, T. and Loader, C. (1993). Local regression: automatic kernel carpentry (with discussion). Statistical Sciences, 120-143.
46. Hermann, E., Gasser, T. and Kneip, A. (1992). Choice of bandwidth for kernel regression when residuals are correlated. Biometrika 79, 783-795.
47. Holiday, D. B. (1986). On nonparametric regression estimation in a correlated errors model. Ph.D. dissertation, Texas A & M University.
48. Holiday, D. B. (1989). The estimation of derivatives of a nonparametric regression function when the data are correlated. Communications in Statistics - Theory and Methods 18, 2107-2124.
49. Hurvich, C. M. and Zeger, S. L. (1990). A frequency domain selection criterion for regression with autocorrelated errors. Journal of the American Statistical Association 85, 705-714.
50. James, W. and Stein, C. (1961). Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics and Probability 1, 361-379. Univ. California Press.
51. Kim, T. and Cox, D. (1992). Asymptotic optimality of simple cross-validation for bandwidth selection in nonparametric regression for stationary mixing observations. Manuscript.
52. King, E., Hart, J. D. and Wehrly, T. E. (1991). Testing the equality of two regression curves using linear smoothers. Statistics and Probability Letters 12, 239-247.
53. Kohn, R., Ansley, C. G. and Wong, C.-M. (1992). Nonparametric spline regression with autoregressive moving average errors. Biometrika 79, 335-346.
54. Ljung, L. (1978). Convergence analysis of parametric identification methods. IEEE Transactions on Automatic Control 23, 770-783.
55. Lombard, F. and Hart, J. D. (1994). The analysis of changepoint data with dependent errors. In Change-point Problems (E. Carlstein, H.-G. Müller, and D. Siegmund, eds.) 194-209. Institute of Mathematical Statistics Lecture Notes-Monograph Series 23.
56. Masry, E. (1986). Recursive probability density estimation for weakly dependent processes. IEEE Transactions on Information Theory 32, 254-267.
57. Masry, E. and Györfi, L. (1987). Strong consistency and rates for recursive density estimators for stationary mixing processes. Journal of Multivariate Analysis 22, 79-93.
58. Müller, H.-G. (1988). Nonparametric Regression Analysis of Longitudinal Data. Lecture Notes in Statistics 46. Springer-Verlag, Heidelberg.
59. Müller, H.-G. and Stadtmüller, U. (1988). Detecting dependencies in smooth regression models. Biometrika 75, 639-650.
60. Newton, H. J. (1988). Timeslab: A Time Series Analysis Laboratory. Wadsworth and Brrooks/Cole, Pacific Grove, California.
61. Park, B.U. and Marron, J. S. (1990). Comparison of data-driven bandwidth selectors. Journal of the American Statistical Association 85, 66-72.
62. Prakasa Rao, B. L. S. (1977). Berry-Esseen bound for density estimators of stationary Markov processes. Bulletin of Mathematical Statistics 17, 15-21.
63. Prakasa Rao, B. L. S. (1983). Nonparametirc Functional Estimation. Academic Press, Orlando, Florida.
64. Priestly, M. B. (1981). Spectral Analysis and Time Series. Academic Press, London.
65. Raz, J. (1989). Analysis of repeated measurements using nonparametric smoothers and randomization tests. Biometrics 45, 851-871.
66. Raz, J., Turetsky, B. and Fein, G. (1989). Selecting the smoothing parameter for estimation of slowly changing evoked potential signals. Biometrics 45, 745-762.
67. Rice, J. A. and Silverman, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society B 53, 233-244.
68. Robinson, P. M. (1983). Nonparametric estimates for time series. Journal of Time Series Analysis 4, 185-201
69. Robinson, P. M. (1984). Kernel estimation and interpolation for time series containing missing observations. Annals of the Institute of Statistical Mathematics, Part A 36, 403-417.
70. Rosenblatt, M. (1970). Density estimates and Markov sequences. In Nonparametric Techniques in Statistical Inference. (M. L. Puri, ed.) 199-213. Cambridge University Press.
71. Roussas, G. G. (1969). Nonparametric estimation in Markov processes. Annals of the Institute of Statistical Mathematics 21, 73-87.
72. Rudemo, M. (1982). Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics 9, 65-78.
73. Scott, D. W. and Terrell, G. R. (1987). Biased and unbiased cross-validation in density estimation. Journal of the American Statistical Association 82, 1131-1146.
74. Seillier-Moiseiwitsch, F., Sweeting, T. J. and Dawid, A. P. (1992). Prequential tests of model fit. Scandinavian Journal of Statistics 19, 45-60.
75. Sheather, S. J. (1983). A data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics and Data Analysis 1, 229-238.
76. Sheather, S. J. (1986). An improved data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics and Data Analysis 4, 61-65.
77. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
78. Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proceedings of the Third Berkeley Symposium on Mathematics, Statistics and Probability 1, 197-206. Univ. California Press.
79. Stone, C. J. (1984). An asymptotically optimal window selection rule for kernel density estimates. Annals of Statistics 12, 1285-1297.
80. Tran, L. T. (1992). Kernel density estimation for linear processes. Stochastic Processes and their Applications 41, 281-296.
81. Truong, Y. K. and Stone, C. J. (1992). Nonparametric function estimation involving time series. Annals of Statistics 20, 77-97.
82. Wand, M. P. (1992). Finite sample performance of density estimators under moving average dependence. Statistics and Probability Letters 13, 109-115.
83. Wehrly, T. E. and Hart, J. D. (1988). Bandwidth selection for kernel estimators of growth curves with correlated errors (abstract). Institute of Mathematical Statistics Bulletin 17, 236.
84. Wu, J. S. and Chu, C. K. (1994). Nonparametric estimation of a regression function with dependent observations. Stochastic Processes and their Applications 50, 149-160.
85. Yakowitz, S. (1979). Nonparametric estimation of Markov transition functions. Annals of Statistics 7 671-679.
86. Yakowitz, S. (1985). Nonparametric density estimation, prediction, and regression for Markov sequences. Journal of the American Statistical Association 80, 215-221.
87. Young, S. G. and Bowman, A. W. (1993). Nonparametric analysis of covariance. Biometrics, to appear.