Adaptive tests of linear hypotheses by model selection

Annals of Statistics

Volumn 31, Issue 1, 2003, Pages 225-251

  Baraud, Y ^a,d   Huet, S ^b,e   Laurent, B ^c  

^a ÉCOLE NORMALE SUPÉRIEURE   (France)

^b Laboratoire de Biométrie   (France)

^c UNIVERSITÉ PARIS SACLAY   (France)

^d ECOLE NORMALE SUPÉRIEURE   (France)

^e CEMAGREF   (France)

Author keywords

Adaptive test; Fisher test; Fisher's quantiles; Goodness of fit; Linear hypothesis; Minimax hypothesis testing; Model selection; Nonparametric alternative; Nonparametric regression

Indexed keywords

EID: 21144438312     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1046294463     Document Type: Article

References (23)

1. BARAUD, Y. (2000a). Model selection for regression on a fixed design. Probab. Theory Related Fields 117 467-493.
2. BARAUD, Y. (2000b). Nonasymptotic minimax rates of testing in signal detection. Technical Report 00.25, Ecole Normale Supérieure, Paris.
3. BARAUD, Y., HUET, S. and LAURENT, B. (2001). Nonparametric smoothing and lack-of-fit tests. In Goodness-of-fit Tests and Model Validity (C. Huber-Carol, N. Balakrishnan, M. S. Nikulin and M. Mesbah, eds.) 193-204. Birkhäuser, Boston.
4. BIRGÉ, L. (2001). An alternative point of view on Lepski's method. In State of the Art in Probability and Statistics (Leiden, 1999) 113-133. IMS, Beachwood, OH.
5. BIRGÉ, L. and MASSART, P. (2001). Gaussian model selection. J. Eur. Math. Soc. 3 203-268.
6. CASTELLAN, G. (2000). Density estimation via exponential model selection. Technical Report 00.25, Univ. Paris XI, Orsay.
7. CHEN, J.-C. (1994). Testing for no effect in nonparametric regression via spline smoothing techniques. Ann. Inst. Statist. Math. 46 251-265.
8. DETTE, H. and MUNK, A. (1998). Validation of linear regression models. Ann. Statist. 26 778-800.
9. EUBANK, R. L. and HART, J. D. (1992). Testing goodness-of-fit in regression via order selection criteria. Ann. Statist. 20 1412-1425.
10. EUBANK, R. L. and LARICCIA, V. N. (1993). Testing for no effect in nonparametric regression. J. Statist. Plann. Inference 36 1-14.
11. GASSER, T., SROKA, L. and JENNEN-STEINMETZ.C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika 73 625-633.
12. HÄRDLE, W. and MAMMEN, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 1926-1947.
13. HART, J. D. (1997). Nonparametric Smoothing and Lack-of-fit Tests. Springer, New-York.
14. HOROWITZ, J. L. and SPOKOINY, V. G. (2001). An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69 599-631.
15. INGLOT, T. and LEDWINA, T. (1996). Asymptotic optimality of data-driven Neyman's tests for uniformity. Ann. Statist. 24 1982-2019.
16. INGSTER, YU. I. (1993). Asymptotically minimax testing for nonparametric alternatives I. Math. Methods Statist. 2 85-114.
17. INGSTER, YU. I. and SUSLINA, I. A. (1998). Minimax detection of a signal for Besov bodies and balls. Problems Inform. Transmission 34 48-59.
18. LAURENT, B. and MASSART, P. (2000). Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 1302-1338.
19. LEPSKI, O. V. and SPOKOINY, V. G. (1999). Minimax nonparametric hypothesis testing: The case of inhomogeneous alternative. Bernoulli 5 333-358.
20. MÜLLER, H.-G. (1992). Goodness-of-fit diagnostics for regression models. Scand. J. Statist. 19 157-172.
21. NISHII, R. (1988). Maximum likelihood principle and model selection when the true model is unspecified. J. Multivariate Anal 27 392-403.
22. SPOKOINY, V. G. (1996). Adaptive hypothesis testing using wavelets. Ann. Statist. 24 2477-2498.
23. STANISWALIS, J. G. and SEVERINI, T. A. (1991). Diagnostics for assessing regression models. J. Amer. Statist. Assoc. 86 684-692.