Asymptotic optimality of new adaptive test in regression model
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 5, p. 579-590
@article{AIHPB_2006__42_5_579_0,
author = {Inglot, Tadeusz and Ledwina, Teresa},
title = {Asymptotic optimality of new adaptive test in regression model},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
publisher = {Elsevier},
volume = {42},
number = {5},
year = {2006},
pages = {579-590},
doi = {10.1016/j.anihpb.2005.05.002},
zbl = {1098.62053},
mrnumber = {2259976},
language = {en},
url = {http://www.numdam.org/item/AIHPB_2006__42_5_579_0}
}

Inglot, Tadeusz; Ledwina, Teresa. Asymptotic optimality of new adaptive test in regression model. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 5, pp. 579-590. doi : 10.1016/j.anihpb.2005.05.002. http://www.numdam.org/item/AIHPB_2006__42_5_579_0/

[1] Y. Baraud, S. Huet, B. Laurent, Adaptive tests of linear hypotheses by model selection, Ann. Statist. 31 (2003) 225-251. | MR 1962505 | Zbl 1018.62037

[2] L. Birgé, An alternative point of view on Lepski's method, in: State of the Art in Probability and Statistics, Leiden 1999, IMS, Beachwood, OH, 2001, pp. 113-133. | MR 1836557

[3] G.R. Ducharme, T. Ledwina, Efficient and adaptive nonparametric test for the two-sample problem, Ann. Statist. 31 (2003) 2036-2058. | MR 2036399 | Zbl 1065.62079

[4] R.L. Eubank, Testing for no effect by cosine series methods, Scand. J. Statist. 27 (2000) 747-763. | MR 1804174 | Zbl 0962.62031

[5] R.L. Eubank, J.D. Hart, Testing goodness of fit in regression via order selection criteria, Ann. Statist. 20 (1992) 1412-1425. | MR 1186256 | Zbl 0776.62045

[6] J. Fan, L.-S. Huang, Goodness-of-fit tests for parametric regression models, J. Amer. Statist. Assoc. 96 (2001) 640-652. | MR 1946431 | Zbl 1017.62014

[7] T. Inglot, On large deviation theorem for data driven Neyman's statistic, Statist. Probab. Lett. 47 (2000) 487-509. | MR 1766868 | Zbl 0945.62054

[8] T. Inglot, W.C.M. Kallenberg, T. Ledwina, Vanishing shortcoming of data driven Neyman's tests, in: Asymptotic Methods in Probability and Statistics, A Volume to Honour Miklós Csörgő, Elsevier, Amsterdam, 1998, pp. 811-829. | MR 1661520 | Zbl 0956.62040

[9] T. Inglot, T. Ledwina, Asymptotic optimality of data driven smooth tests for location-scale family, Sankhyā Ser. A 63 (2001) 41-71. | MR 1898549 | Zbl 0999.62034

[10] T. Inglot, T. Ledwina, Intermediate approach to comparison of some goodness-of-fit tests, Ann. Inst. Statist. Math. 53 (2001) 810-834. | MR 1880814 | Zbl 1003.62042

[11] T. Inglot, T. Ledwina, On consistent minimax distinguishability and intermediate efficiency of Cramér-von Mises test, J. Statist. Plann. Inference 124 (2004) 453-474. | MR 2081497 | Zbl 1047.62037

[12] T. Inglot, T. Ledwina, Intermediate efficiency of some max-type statistics, J. Statist. Plann. Inference (2006), in press. | MR 2256213 | Zbl 1094.62021

[13] T. Inglot, T. Ledwina, Towards data driven selection of penalty function for data driven Neyman tests, Linear Algebra Appl. (2005), in press. | Zbl 1095.62023

[14] N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous Univariate Distributions, vol. 1, Wiley Interscience, New York, 1994. | MR 1299979 | Zbl 0821.62001

[15] W.C.M. Kallenberg, Asymptotic Optimality of Likelihood Ratio Tests in Exponential Families, Math. Centre Tracts, vol. 77, CWI, Amsterdam, 1978. | MR 488460 | Zbl 0497.62028

[16] W.C.M. Kallenberg, The penalty in data driven Neyman's tests, Math. Methods Statist. 11 (2002) 323-340. | MR 1964450

[17] Ya.Yu. Nikitin, On the Hodges-Lehmann asymptotic efficiency of nonparametric tests of goodness-of-fit and homogeneity, Theory Probab. Appl. 32 (1987) 77-88. | MR 890933 | Zbl 0642.62032

[18] Ya.Yu. Nikitin, Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press, New York, 1995. | MR 1415127 | Zbl 0879.62045

[19] J. Oosterhoff, Combination of One-Sided Statistical Tests, Mathematical Centre, Amsterdam, 1969. | MR 247707 | Zbl 0193.15901

[20] J. Oosterhoff, W.R. Van Zwet, The likelihood ratio test for the multinomial distribution, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. I, 1972, pp. 31-50. | MR 397956 | Zbl 0233.62007