Adaptive drift estimation for nonparametric diffusion model

Annals of Statistics

Volumn 28, Issue 3, 2000, Pages 815-836

  Spokoiny, Vladimir G ^a,b  

^a Weierstrass Inst Appl Anal S   (Germany)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Bandwidth selection; Drift and diffusion coefficients; Nonparametric estimation

Indexed keywords

EID: 0034362824     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015951999     Document Type: Article

References (31)

1. BROWN, L. D. and Low, M. G (1996). A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist. 24 2524-2535.
2. COLLOMB, G. and DOUKHAN, P. (1983). Estimation non parametrique de la fonction d'autoregression d'un processus stationnaire et phi melangeant: risques quadratiques pour la methode du noyau. C.R. Acad. Sci. Paris Sér. I 296 859-862.
3. DAHLHAUS, R. (1997). Fitting time series to nonstationary processes. Ann. Statist. 25 1-37.
4. DELYON, B. and JUDITSKY, A. (2000). On minimax identification of nonparametric autoregressive models. Probab. Theory Relat. Fields 116 21-39.
5. DONOHO, D. L. and JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455.
6. n". C.R. Acad. Sci. Paris Sér. A 291 61-64.
7. DOUKHAN, P. and TSYBAKOV, A. B. (1993). Nonparametric recurrent estimation in nonlinear ARX models. Problems Inform. Transmission 29 318-327.
8. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and Its Applications. Chapman and Hall, London.
9. FAN, J. and YAO, Q. (1988). Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85 645-660.
10. GENON-CATALOT, V., LAREDO, C. and PICARD, D. (1992). Nonparametric estimation of the diffusion coefficient by wavelet methods. Scared. J. Statist. 19 317-335.
11. HALL, P. and CARROLL, R. J. (1989). Variance function estimation in regression: the effect of estimation of the mean. J. Roy. Statist. Soc. Ser. B 51 3-14.
12. HÄRDLE, W. and TSYBAKOV, A. (1997). Local polynomial estimators of the volatility function in nonparametric autoregression. J. Econometrics 81 233-242.
13. HÄRDLE, W. and VIEU, P. (1992). Kernel regression smoothing of time series. J. Time Ser. Anal. 13 209-232.
14. GRAMA, I. and NUSSBAUM, M. (1998). Asymptotic equivalence for nonparametric generalized linear models. Probab. Theory Related Fields 111 107-214.
15. IBRAGIMOV, J. A. and KHASMINSKII, R. Z. (1981). Statistical Estimation: Asymptotic Theory. Springer, New York.
16. KATKOVNIK, V. JA. (1985). Nonparametric Identification and Data Smoothing: Local Approximation Approach (in Russian). Nauka, Moscow.
17. KUTOYANTS, YU. A. (1984a). On nonparametric estimation of trend coefficients in a diffusion process. In Statistics and Control of Stochastic Processes 230-250. Moscow.
18. KUTOYANTS, YU. A. (1984b). Parameter estimation for stochastic processes. In R & E Research and Exposition in Mathematics 6 (B. L. S. Prakasa, Rao ed.) Heldermann, Berlin.
19. LEPSKI, O. (1990). One problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35 459-470.
20. LEPSKI, O. and LEVIT, B. (1997). Efficient adaptive estimation of infinitely differentiable function. Unpublished manuscript.
21. LEPSKI, O., MAMMEN, E. and SPOKOINY, V. (1997). Ideal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selection. Ann. Statist. 25 929-947.
22. LEPSKI, O. and SPOKOINY, V. (1997). Optimal pointwise adaptive methods in nonparametric estimation. Ann. Statist. 25 2512-2546.
23. LIPTSER, R. and SHIRYAEV, A. (1989). Theory of Martingales. Kluwer, Dordrecht.
24. MERCURIO, D. and SPOKOINY, V. (2000). Statistical inference for time-inhomogeneous volatility models. http: //www.wias-berlin.de WIAS preprint 583, Berlin.
25. MILSTEIN, G. and NUSSBAUM, M. (1994). Nonparametric estimation of a nonparametric diffusion model. Probab. Theory Related Fields. 112 535-543.
26. NEUMANN, M. H. (1998). Strong approximation of density estimators from weakly dependent observations by density estimators from independent observations. Ann. Statist. 26 2014-2048.
27. RUPPERT, D., WAND, M. P., HOLST, U. and HÖSSJER, O. (1997). Local polynomial variance function estimation. Technometrics 39 262-273.
28. SPOKOINY, V. (1996). Adaptive hypothesis testing using wavelets. Ann. Statist. 24 2477-2498.
29. SPOKOINY, V. (1998) Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice. Ann. Statist. 26 1356-1378.
30. TSYBAKOV, A. (1986). Robust reconstruction of functions by the local approximation. Problems Inform. Transmission 22 133-146.
31. VERETENNIKOV, A. YU. (1991). On the averaging principle for systems of stochastic differential equations. Math. USSR Sborn. 69 271-284.