Root n bandwidth selectors for kernel estimation of density derivatives

Journal of the American Statistical Association

Volumn 92, Issue 438, 1997, Pages 536-547

  Wu, Tiee Jian ^a,b  

^a University of Houston   (United States)

^b NATIONAL DONG HWA UNIVERSITY   (Taiwan)

Author keywords

Characteristic function; Information bound; Plug in method; Smoothed cross validation

Indexed keywords

EID: 0031490295     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10474006     Document Type: Article

References (41)

1. Bowman, A. (1984), "An Alternative Method of Cross-Validation for the Smoothing of Density Estimates," Biometrika, 71, 353-360.
2. Chiu, S. T. (1991a), "Bandwidth Selection for Kernel Density Estimation," The Annals of Statistics, 19, 1883-1905.
3. Chiu, S. T (1991b), "The Effect of Discretization Error on Bandwidth Selection for Kernel Density Estimation," Biometrika, 78, 436-441.
4. Chiu, S. T (1992), "An Automatic Bandwidth Selector for Kernel Density Estimation," Biometrika, 79, 771-782. Journal of the American Statistical Association, June 1997
5. Davis, K. B. (1975), "Mean Square Error Properties of Density Estimates," The Annals of Statistics, 3, 1025-1030.
6. Davis, K. B (1977), "Mean Integrated Square Error Properties of Density Estimates," The Annals of Statistics, 5, 530-535.
7. Fan, J., and Marron, J. S. (1992), "Best Possible Constant for Bandwidth Selection;' The Annals of Statistics, 20, 2057-2070.
8. Grund, B., Ball, P., and Marron, I. S. (1994), "Loss and Risk in Smoothing Parameter Selection," Journal of Nonparametric Statistics, 4, 107-132.
9. Hall, P. (1983), "Large Sample Optimality of Least Squares CrossValidation in Density Estimation," The Annals of Statistics, 11, 1156-1174.
10. Hall, P., and Marron, J. S. (1987), "Extent to Which Least-Squares CrossValidation Minimises Integrated Square Error in Nonparametric Density Estimation," Probability Theory and Related Fields, 74, 567-581.
11. Hall, P., and Marron, J. S. (1988), "Choice of Kernel Order in Density Estimation;' The Annals of Statistics, 16, 161-173.
12. Hall, P., and Marron, J. S. (1991a), "Lower Bounds for Bandwidth Selection in Density Estimation," probability Theory and Related Fields, 90, 149-173.
13. Hall, P., and Marron, J. S. (1991b), "Local Minimum in Cross-Validation Functions," Journal of the Royal Statistical Society, Ser. B, 53, 245-252.
14. Hall, P., Marron, J. S., and Park, B. D. (1992), "Smoothed CrossValidation," Probability Theory and Related Fields, 92, 1-20.
15. 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, 521-530.
16. HardIe, w., Hart, J., Marron, J. S., and Tsybakov, A. B. (1992), "Bandwidth Choice for Average Derivative Estimation," Journal of the American Statistical Association, 87, 218-226.
17. HardIe, w., Marron, J. S., and Wand, M. P. (1990), "Bandwidth Choice for Density Derivatives," Journal of the Royal Statistical Society, Ser. B, 52, 223-232.
18. Hardie, w., and Stoker, T. (1989), "Investigating Smooth Multiple Regression by the Method of Average Derivatives," Journal of the American Statistical Association, 84, 986-995.
19. Hewitt, E., and Stromberg, K. (1969), Real and Abstract Analysis, New York: Springer-Verlag.
20. Hildenbrand, K., and Hildenbrand, W. (1986), "On the Mean Income Effect: A Data Analysis of the D.K. Family Expenditure Survey," in Contributions to Mathematical Economics, in Honor of Gerard Debreu, eds. W. Hildenbrand and A. Mas-Colell, Amsterdam: North-Holland, pp. 247-268.
21. Ibragimov, I. A., and Khas'minskii, R. Z. (1982), "Estimation of Distribution Density Belonging to a Class of Entire Functions," Theory of Probability and Its Applications, 27, 551-562.
22. Jones, M. C. (1991), "The Role of ISE and MISE in Density Estimation," Statistics and Probability Letters, 12, 51-56.
23. Jones, M. C, Marron, J. S., and Park, B. D. (1991), "A Simple Root n Bandwidth Selector," The Annals of Statistics, 19, 1919-1932.
24. Jones, M. C., Marron, J. S., and Sheather, S. J. (1996), "A Brief Survey of Bandwidth Selection for Density Estimation," Journal of the American Statistical Association, 91, 401-407.
25. Jones, M. C, and Sheather, S. J. (1991), "Using Non-Stochastic Terms to Advantage in Kernel-Based Estimation of Integrated Squared Density Derivatives," Statistics and Probability Letters, 11, 511-514.
26. Loader, C. R. (1995), "Old Faithful Erupts: Bandwidth Selection Reviewed," unpublished manuscript, AT&T Bell Laboratories.
27. Marron, J. S. (1988), "Automatic Smoothing Parameter Selection: A Survey," Empirical Economics, 13, 187-208.
28. Marron, J. S., and Wand, M. P. (1992), "Exact Mean Integrated Squared Error," The Annals of Statistics, 20, 712-736.
29. Park, B. D., and Marron, J. S.(1990), "Comparison of Data-Driven Bandwidth Selectors," Journal of the American Statistical Association, 85, 66-78.
30. Park, B. D., and Marron, J. S (1992), "On the Use of Pilot Estimators in Bandwidth Selection;' Journal of Nonparametric Statistics, 1, 231-240.
31. Rudemo, M. (1982), "Empirical Choice of Histograms and Kernel Density Estimators," Scandinavian Journal of Statistics, 9, 65-78.
32. Scott, D. W. (1992), Multivariate Density Estimation: Theory, Practice, and Visualization, New York: Wiley.
33. Scott, D. W, and Factor, L. E. (1981), "Monte Carlo Study of Three DataBased Nonparametric Probability Density Estimators," Journal of the American Statistical Association, 76, 9-15.
34. Scott, D. W, Tapia, R. A, and Thompson, J. W(1977), "Kernel Density Estimation Revisited," Journal of Nonlinear Analysis, Theory, Methods and Applications, 1, 339-372.
35. Scott, D. W., and Terrell, G. R. (1987), "Biased and Unbiased CrossValidation in Density Estimation," Journal of the American Statistical Association, 82, 1131-1146.
36. Sheather, S. J., and Jones, M. C. (1991), "A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation," Journal of the Royal Statistical Society, Ser. B, 53, 683-690
37. Silverman, B. W. (1982), "Kernel Density Estimation Using the Fast Fourier Transform," Applied Statistics, 31, 93-99.
38. Stone, C. J. (1980); "Optimal Convergence Rates for Nonparametric Estimators," The Annals ofStatistics, 8, 1348-1360.
39. Stone, C. J (1984), "An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates," The Annals of Statistics, 12, 1285-1297.
40. Woodroofe, M. (1970), "On Choosing a Delta Sequence," Annals ofMathematical Statistics, 41, 1665-1671.
41. Wu, T.-J. (1995), "Adaptive Root n Estimates of Integrated Squared Density Derivatives," The Annals of Statistics, 23, 1474-1495.