Asymptotic distributions of error density and distribution function estimators in nonparametric regression

Journal of Statistical Planning and Inference

Volumn 128, Issue 2, 2005, Pages 327-349

  Cheng, Fuxia ^a  

^a ILLINOIS STATE UNIVERSITY   (United States)

Author keywords

Empirical process; Histogram density estimation; Nonparametric residuals

Indexed keywords

EID: 8644254345     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2003.12.004     Document Type: Article

References (22)

1. Akritas M.G. Van Keilegom I. Non-parametric estimation of the residual distribution Scand. J. Statist. 28 2001 549-567
2. Bickel P.J. Rosenblatt M. On some global measures of the deviations of density function estimators Ann. Statist. 6 1973 1071-1095
3. Boldin M.V. Estimation of the distribution of noise in an autoregression scheme Theory Prob. Appl. 27 1982 866-871
4. Cheng F. Consistency of error density and distribution function estimation in nonparametric regression Statist. & Probab. Lett. 59 2002 257-270
5. Cheng, F., 2002b. Weak and strong uniform consistency of a kernel error density estimate in nonparametric regression, J. Statist. Planning and Inference, in Press.
6. Dvoretzky A. Kiefer J. Wolfowitz J. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator Ann. Math. Statist. 27 1956 642-669
7. Hoeffding W. Probability inequalities for sums of bounded random variables J. Amer. Statist. Assoc. 58 1963 13-30
8. Kallenberg O. Foundations of Modern Probability 1997 Springer New York/Berlin/Heidelberg
9. Koul H.L. Some convergence theorems for ranks and weighted empirical cumulatives Ann. Math. Statist. 41 1970 1768-1773
10. Koul H.L. Behavior of robust estimators in the regression model with dependent errors Ann. Statist. 5 1977 681-699
11. Koul H.L. A weak convergence result useful in robust autoregression J. Statist. Plann. Inference 29 1991 291-308
12. Koul H.L. Weighted Empiricals and Linear Models Lecture Notes-Monograph Series Vol. 21 1992 Institute of Mathematical Statistics Hayward, CA
13. Koul H.L. Asymptotics of some estimators and sequential empiricals in non-linear time series Ann. Statist. 24 1996 380-404
14. Koul H.L. Osiander M. Weak convergence of randomly weighted residuals empiricals with application to autoregression Ann. Statist. 22 1994 540-562
15. Loynes R.M. The empirical d.f. of residuals from generalized regression Ann. Statist. 8 1980 285-298
16. Mammen E. Empirical process of residuals for high-dimensional linear models Ann. Statist. 24 1996 307-335
17. Massart P. The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality Ann. Probab. 18 1990 1269-1283
18. Nadaraya E.A. On estimating regression Theory Probab. Appl. 9 1964 141-142
19. Pollard D. Convergence of Stochastic Process 1984 Springer New York
20. Portnoy S. Asymptotic behavior of the empirical distribution of M-estimated residuals from a regression model with many parameters Ann. Statist. 14 1986 1152-1170
21. van der Vaart A.W. Asymptotic Distribution 1998 Cambridge University Press Cambridge
22. van der Vaart A.W. Wellner J.A. Weak Convergence and Empirical Processes 1996 Springer New York