Model selection for (AUTO–)regression with dependent data

ESAIM - Probability and Statistics

Volumn 5, Issue , 2001, Pages 33-49

  Baraud, Yannick ^a   Comte, F ^b   Viennet, G ^c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Adaptive estimation; Autoregression; Least squares estimator; Mixing processes; Nonparametric regression

Indexed keywords

EID: 84996128104     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps:2001101     Document Type: Article

References (31)

1. H. Akaike, Information theory and an extension of the maximum likelihood principle, in Proc. 2nd International Symposium on Information Theory, edited by P.N. Petrov and F. Csaki. Akademia Kiado, Budapest (1973) 267-281.
2. H. Akaike, A new look at the statistical model identification. IEEE Trans. Automat. Control 19 (1984) 716-723.
3. P. Ango Nze, Geometric and subgeometric rates for markovian processes in the neighbourhood of linearity. C. R. Acad. Sci. Paris 326 (1998) 371-376.
4. Y. Baraud, Model selection for regression on a fixed design. Probab. Theory Related Fields 117 (2000) 467-493.
5. Y. Baraud, Model selection for regression on a random design, Preprint 01-10. DMA, Ecole Normale Superieure (2001).
6. Y. Baraud, F. Comte and G. Viennet, Adaptive estimation in autoregression or ^-mixing regression via model selection. Ann. Statist. (to appear).
7. A. Barron, L. Birge and P. Massart, Risks bounds for model selection via penalization. Probab. Theory Related Fields 113 (1999) 301-413.
8. L. Birge and P. Massart, An adaptive compression algorithm in Besov spaces. Constr. Approx. 16 (2000) 1-36.
9. L. Birge and Y. Rozenholc, How many bins must be put in a regular histogram. Working paper (2001).
10. A. Cohen, I. Daubechies and P. Vial, Wavelet and fast wavelet transform on an interval. Appl. Comput. Harmon. Anal. 1 (1993) 54-81.
11. I. Daubechies, Ten lectures on wavelets. SIAM: Philadelphia (1992).
12. R.A. Devore and C.G. Lorentz, Constructive Approximation. Springer-Verlag (1993).
13. D.L. Donoho and I.M. Johnstone, Minimax estimation via wavelet shrinkage. Ann. Statist. 26 (1998) 879-921.
14. P. Doukhan, Mixing properties and examples. Springer-Verlag (1994).
15. M. Duflo, Random Iterative Models. Springer, Berlin, New-York (1997).
16. M. Hoffmann, On nonparametric estimation in nonlinear AR(1)-models. Statist. Probab. Lett. 44 (1999) 29-45.
17. I.A. Ibragimov, On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition I: Necessary conditions. Theory Probab. Appl. 10 (1965) 85-106.
18. M. Kohler, On optimal rates of convergence for nonparametric regression with random design, Working Paper. Stuttgart University (1997).
19. A.R. Kolmogorov and Y.A. Rozanov, On the strong mixing conditions for stationary Gaussian sequences. Theory Probab. Appl. 5 (1960) 204-207.
20. K.C. Li, Asymptotic optimality for Cp, C\ cross-validation and generalized cross-validation: Discrete index set. Ann. Statist. 15 (1987) 958-975.
21. G.G. Lorentz, M. von Golitschek and Y. Makokov, Constructive Approximation, Advanced Problems. Springer, Berlin (1996).
22. C. L. Mallows, Some comments on Cp. Technometrics 15 (1973) 661-675.
23. A. Meyer, Quelques inégalités sur les martingales d’après Dubins et Freedman, Seminaire de Probabilites de l’Université de Strasbourg. Vols. 6869 (1969) 162-169.
24. D. S. Modha and E. Masry, Minimum complexity regression estimation with weakly dependent observations. IEEE Trans. Inform. Theory 42 (1996) 2133-2145.
25. D.S. Modha and E. Masry, Memory-universal prediction of stationary random processes. IEEE Trans. Inform. Theory 44 (1998) 117-133.
26. M. Neumann and J.-P. Kreiss, Regression-type inference in nonparametric autoregression. Ann. Statist. 26 (1998) 1570-1613.
27. B. T. Polyak and A. Tsybakov, A family of asymptotically optimal methods for choosing the order of a projective regression estimate. Theory Probab. Appl. 37 (1992) 471-481.
28. R. Shibata, Selection of the order of an autoregressive model by Akaike’s information criterion. Biometrika 63 (1976) 117-126.
29. R. Shibata, An optimal selection of regression variables. Biometrika 68 (1981) 45-54.
30. S. Van de Geer, Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes. Ann. Statist. 23 (1995) 1779-1801.
31. V.A. Volonskii and Y.A. Rozanov, Some limit theorems for random functions. I. Theory Probab. Appl. 4 (1959) 179-197.