Estimating linear functionals of the error distribution in nonparametric regression

Journal of Statistical Planning and Inference

Volumn 119, Issue 1, 2004, Pages 75-93

  Müller, Ursula U ^a   Schick, Anton ^b   Wefelmeyer, Wolfgang ^c  

^a UNIVERSITY OF BREMEN   (Germany)

^b BINGHAMTON UNIVERSITY   (United States)

^c UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Efficient estimator; Influence function; Leave one out estimator; Locally polynomial smoother; Nonparametric regression estimator; Variance estimator

Indexed keywords

EID: 0242720189     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00412-3     Document Type: Article

References (39)

1. Akritas M.G. Van Keilegom I. Non-parametric estimation of the residual distribution Scand. J. Statist. 28 2001 549-567
2. Bai J. Weak convergence of the sequential empirical processes of residuals in ARMA models Ann. Statist. 22 1994 2051-2061
3. Bickel P.J. Klaassen C.A.J. Ritov Y. Wellner J.A. Efficient and Adaptive Estimation for Semiparametric Models 1998 Springer New York
4. Birgé L. Massart P. Estimation of integral functionals of a density Ann. Statist. 23 1995 11-29
5. Boldin M.V. Estimation of the distribution of noise in an autoregression scheme Theory Probab. Appl. 27 1982 866-871
6. 2 criteria Soviet Math. Dokl. 28 1983 550-553
7. 2 tests Theory Probab. Appl. 34 1989 699-704
8. Boldin M.V. On residual empirical distribution functions in ARCH models with applications to testing and estimation Mitt. Math. Sem. Giessen 235 1998 49-66
9. Buckley M.J. Eagleson G.K. Silverman B.W. The estimation of residual variance in nonparametric regression Biometrika 75 1988 189-199
10. Carter C.K. Eagleson G.K. A comparison of variance estimators in nonparametric regression J. Roy. Statist. Soc. Ser. B. (Methodological) 54 1992 773-780
11. Dette H. Munk A. Wagner T. Estimating the variance in nonparametric regression-what is a reasonable choice? J. Roy. Statist. Soc. Ser. B. (Methodological) 60 1998 751-764
12. Dette, H., Munk, A., Wagner, T., 1999. A review of variance estimators with extensions to multivariate nonparametric regression models. In: Ghosh, S. (Ed.), Multivariate Analysis, Design of Experiments, and Survey Sampling, Statistics: Textbooks and Monographs 159. Dekker, New York, pp. 469-498.
13. Efromovich S. Samarov A. Adaptive estimation of the integral of squared regression derivatives Scand. J. Statist. 27 2000 335-351
14. Eggermont P.P.B. LaRiccia V.N. Best asymptotic normality of the kernel density entropy estimator for smooth densities IEEE Trans. Inform. Theory 45 1999 1321-1326
15. Ghoudi K. Rémillard B. Empirical processes based on pseudo-observations In: Szyszkowicz B. (Ed.) Asymptotic Methods in Probability and Statistics 1998 171-197 North-Holland Amsterdam
16. Goldstein L. Messer K. Optimal plug-in estimators for nonparametric functional estimation Ann. Statist. 20 1995 1306-1328
17. Hájek J. Sidák Z. Theory of Rank Tests 1967 Academic Press New York
18. Hall P. Kay J.W. Titterington D.M. Asymptotically optimal difference-based estimation of variance in nonparametric regression Biometrika 77 1990 521-528
19. Hall P. Marron J.S. On variance estimation in nonparametric regression Biometrika 77 1990 415-419
20. Ibragimov I.A. Has'minskii R.Z. Statistical Estimation. Asymptotic Theory Applications of Mathematics Vol. 16 1981 Springer New York
21. Koshevnik Yu.A. Semiparametric estimation of a symmetric error distribution from regression models Publ. Inst. Statist. Univ. Paris 40 1996 77-91
22. Koul H.L. Asymptotic behavior of Wilcoxon type confidence regions in multiple linear regression Ann. Math. Statist. 40 1969 1950-1979
23. Koul H.L. Some convergence theorems for ranks and weighted empirical cumulatives Ann. Math. Statist. 41 1970 1768-1773
24. Koul H.L. Tests of goodness-of-fit in linear regression Colloq. Math. Soc. János Bolyai 45 1987 279-315
25. Koul H.L. Asymptotics of some estimators and sequential residual empiricals in nonlinear time series Ann. Statist. 24 1996 380-404
26. Koul H.L. Weighted Empirical Processes in Dynamic Nonlinear Models Lecture Notes in Statistics Vol. 166 2002 Springer New York
27. Koul H.L. Levental S. Weak convergence of the residual empirical process in explosive autoregression Ann. Statist. 17 1989 1784-1794
28. Koul H.L. Ossiander M. Weak convergence of randomly weighted dependent residual empiricals with applications to autoregression Ann. Statist. 22 1994 540-562
29. Koul H.L. Sen P.K. Weak convergence of a weighted residual empirical process in autoregression Statist. Decisions 9 1991 235-262
30. Kreiss J.-P. Estimation of the distribution function of noise in stationary processes Metrika 38 1991 285-297
31. Levit B.Y. Conditional estimation of linear functionals Problems Inform. Transmission 11 1975 39-54
32. Loynes R.M. The empirical distribution function of residuals from generalised regression Ann. Statist. 8 1980 285-299
33. Mammen E. Empirical process of residuals for high-dimensional linear models Ann. Statist. 24 1996 307-335
34. Müller, U.U., Schick, A., Wefelmeyer, W., 2001. Estimating the error variance in nonparametric regression by a covariate-matched U-statistic. Statistics to appear.
35. Schick, A., 1993. On efficient estimation in regression models. Ann. Statist. 21, 1486-1521; Correction and addendum: 23 (1995) 1862-1863.
36. Schick, A., Wefelmeyer, W., 2002. Estimating the innovation distribution in nonlinear autoregressive models. Ann. Inst. Statist. Math. 54, 245-260.
37. Shorack G.R. Empirical and rank processes of observations and residuals Canad. J. Statist. 12 1984 319-332
38. Shorack, G.R., Wellner, J.A., 1986. Empirical Processes with Applications to Statistics. Wiley Series in Probability and Mathematical Statistics. Wiley, New York.
39. Wefelmeyer W. An efficient estimator for the expectation of a bounded function under the residual distribution of an autoregressive process Ann. Inst. Statist. Math. 46 1994 309-315