Simultaneous estimation of the mean and the variance in heteroscedastic Gaussian regression

Electronic Journal of Statistics

Volumn 2, Issue , 2008, Pages 1345-1372

  Gendre, Xavier ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Convergence rate; Gaussian regression; Heteroscedasticity; Kullback risk; Model selection

Indexed keywords

EID: 80051474161     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-EJS267     Document Type: Article

References (19)

1. Akaike, H. (1969). Statistical predictor identification. Annals Inst. Statist. Math.
2. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Proceedings 2nd International Symposium on Information Theory, P. Petrov and F. Csaki, Eds. Akademia Kiado, Budapest, 267-281.
3. Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. On Automatic Control.
4. Arlot, S. (2007). Rééchantillonnage et sélection de modèles. Ph.D. thesis, Université Paris 11.
5. Baraud, Y. (2000). Model selection for regression on a fixed design. Probab. Theory Related Fields 117, 467-493.
6. Baraud, Y., Giraud, C., and Huet, S. (2006). Gaussian model selection with an unknown variance. To appear in Annals of Statistics.
7. Barron, A., Birgé, L., and Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113, 301-413.
8. Birgé, L. And Massart, P. (1997). From model selection to adaptive estimation. Festschrift for Lucien Lecam: Research Papers in Probability and Statistics.
9. Birgé, L. And Massart, P. (2001a). Gaussian model selection. Journal of the European Mathematical Society 3, 3, 203-268.
10. Birgé, L. And Massart, P. (2001b). A generalized cp criterion for gaussian model selection. Prépublication 647, Universités de Paris 6 and Paris 7.
11. Boucheron, S., Bousquet, O., Lugosi, G., and Massart, P. (2005). Moment inequalities for functions of independent random variables. Annals of Probability 33, 2, 514-560.
12. Comte, F. And Rozenholc, Y. (2002). Adaptive estimation of mean and volatility functions in (auto-)regressive models. Stochastic Processes and their Applications 97, 1, 111-145.
13. DeVore, R. And Lorentz, G. (1993). Constructive approximation. Vol. 303. Springer-Verlag.
14. Galtchouk, L. And Pergamenshchikov, S. (2005). Efficient adaptive nonparametric estimation in heteroscedastic regression models. Université Louis Pasteur, IRMA, Preprint.
15. Laurent, B. And Massart, P. (2000). Adaptive estimation of a quadratic functional by model selection. Annals of Statistics 28, 5, 1302-1338.
16. Mallows, C. (1973). Some comments on cp. Technometrics 15, 661-675.
17. McQuarrie, A. And Tsai, C. (1998). Regression and times series model selection. World Scientific Publishing Co, Inc.
18. R Development Core Team. (2007). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.R-project.org.
19. Wang, L. And al. (2008). Effect of mean on variance function estimation in nonparametric regression. The Annals of Statistics 36, 2, 646-664.