Evaluation for moments of a ratio with application to regression estimation

Bernoulli

Volumn 15, Issue 4, 2009, Pages 1259-1286

  Doukhan, Paul ^a   Lang, Gabriel ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b AgroParisTech   (France)

Author keywords

Division; Ratio; Regression estimation; Weighted sums

Indexed keywords

EID: 77649218548     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/09-BEJ190     Document Type: Article

References (29)

1. Ango Nze, P. and Doukhan, P. (1996). Nonparametric minimax estimation in a weakly dependent framework I: Quadratic properties. Math. Methods Statist. 5 404-423. MR1443126
2. Ango Nze, P. and Doukhan, P. (1998). Nonparametric minimax estimation in a weakly dependent framework II: Uniform properties. J. Statist. Plann. Inference 68 5-29. MR 1627588
3. Ango Nze, P. and Doukhan, P. (2004). Weak dependence: Models and applications to econometrics. Econom. Theory 20 995-1045. MR2101950
4. Ango Nze, P., Bühlman, P. and Doukhan, P. (2002). Weak dependence beyond mixing and asymptotics for nonparametric regression. Ann. Statist. 30 397-430. MR 1902893
5. Bensaïd, N. and Fabre, J.-P. (2007). Optimal asymptotic quadratic errors of kernel estimators of Radon-Nikodym derivative for strong mixing data. J. Nonparametr. Stat. 19 77-88. MR2345845
6. Collomb, G. (1977). Quelques propriétés de la méthode du noyau pour l'estimation non paramétrique de la régression en un point fixé. C. R. Acad. Sci. Paris 285 289-292. MR0474612
7. Collomb, G. and Doukhan, P. (1983). Estimation nonparamétrique de la fonction d'autorégression d'un processus stationnaire et Pdbl-mélangeant. C. R. Acad. Sci. Paris 296 859-863. MR0712758
8. Dedecker, J. (2001). Exponential inequalities and functional central limit theorems for random fields. ESAlM Probab. Stat. 5 77-104. Available at http://www.esaim-ps.org. MR 1875665
9. Dedecker, J., Doukhan, P., Lang, G., León, J.R., Louhichi, S. and Prieur, C. (2007). Weak Dependence: Models, Theory and Applications. Lecture Notes in Statist. 190. New York: Springer.
10. Dedecker, J. and Prieur, C (2005). New dependence coefficients. Examples and applications to statistics. Probab. Theory Related Fields 132 203-236. MR2199291
11. de la Peña, V.H., Klass, M.J. and Lai, T.L. (2007). Pseudo-maximization and self-normalized processes. Probab. Surv. 4 172-192. MR2368950
12. Del Moral, P. and Mielo, L. (2000). Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering. In Séminaire de Probabilités XXXIV (J. Azéma, M. Emery, M. Ledoux and M. Yor, eds.). Lecture Notes in Math. 1729 1-145. New York: Springer. MR1768060
13. Doukhan, P. (1994). Mixing: Properties and Examples. Lecture Notes in Statist. 85. New York: Springer. MR 1312160
14. Doukhan, P. and Louhichi, S. (2001). Functional density estimation under a new weak dependence condition. Scand. J. Statist. 28 325-342. MR 1842253
15. Doukhan, P. and Neumann, M. (2007). A Bernstein type inequality for times series. Stochastic Process. Appl. 117 878-903. MR2330724
16. Doukhan, P. and Portal, F. (1983). Moments de variables aléatoires mélangeantes. C. R. Acad. Sci. Paris 297 129-132. MR0720925
17. Doukhan, P. and Wintenberger, O. (2007). Invariance principle for new weakly dependent stationary models under sharp moment assumptions. Probab. Math. Statist. 27 45-73. MR2353271
18. Fearnhead, P. and Liu, Z. (2007). On-line inference for multiple changepoint problems. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 589-605. MR2370070
19. Figiel, T., Hitczenko, P., Johnson, W.B., Schechtmann, G. and Zinn, J. (1997). Extremal properties of Rademacher functions with applications to the Khinchine and Rosenthal inequalities. Trans. Amer. Math. Soc. 349 997-1027. MR 1390980
20. Jaber, M.Y. and Salameh, M.K. (1995). Optimal lot sizing under learning considerations: Shortages allowed and backordered. Appl. Math. Model. 19 307-310.
21. [21] Li, G. and Rabitz, H. (2006). Ratio control variate method for efficiently determining high-dimensional model representations. J. Comput. Chem. 27 1112-1118. (Pubitemid 43989804)
22. Pisier, G. (1978). Some results on Banach spaces without local unconditional structure. Compos. Math. 37 3-19. MR0501916
23. Robert, C.P. and Casella, G. (1999). Monte Carlo Statistical Methods. New York: Springer. MR 1707311
24. Rio, E. (2000). Théorie asymptotique pour des processus aléatoires faiblement dépendants. In SMAI, Mathématiques et Applications 31. Berlin: Springer. MR2117923
25. Spiegelmann, C and Sachs, J. (1980). Consistent window estimation in nonparametric regression. Ann. Statist. 8 240-246. MR0560726
26. Stone, C.J. (1980). Optimal rates of convergence for nonparametric estimators. Ann. Statist. 8 1348-1360. MR0594650
27. Stone, C.J. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10 1040-1053. MR0673642
28. Tsybakov, A.B. (2004). Introduction à l'estimation non-paramétrique. In SMAI, Mathématiques et Applications 41. Berlin: Springer. MR2013911
29. Viennet, G. (1997). Inequalities for absolutely regular sequences: Application to density estimation. Probab. Theory Related Fields 107 467-492. MR1440142