Diffusion approximation for nonparametric autoregression

Probability Theory and Related Fields

Volumn 112, Issue 4, 1998, Pages 535-543

  Milstein, Grigori ^a   Nussbaum, Michael ^a  

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

Author keywords

Asymptotic sufficiency; Autoregression; Deficiency distance; Diffusion sampling; Likelihood ratio process; Nonparametric experiments; Stochastic differential equation

Indexed keywords

EID: 0032263667     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050199     Document Type: Article

References (22)

1. Bosq, D.: Nonparametric Statistics for Stochastic Processes. Lecture Notes in Statistics 110, Springer Verlag, New York (1996)
2. Breiman, L.: Probability. Addison-Wesley, New York (1968)
3. Brown, L.D., and Low, M.: Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 , 2384-2398 (1996)
4. Chan, N.H., and Wei, C.Z.: Asymptotic inference for nearly nonstationary AR(1) processes. Ann. Statist. 15, 1050-1063 (1987)
5. Cox, D.D.: Gaussian likelihood estimation for nearly nonstationary AR(1) processes. Ann. Statist. 19, 1129-1142 (1991)
6. Doukhan, P., and Ghindès, M.: Estimation de la probabilité de transition d'une chaîne de Markov Doëblin-récurrente. Etude du cas du processus autorégressif général d'ordre 1. Stochastic Processes Appl. 15, 271-292 (1983)
7. Genon-Catalot, V., and Larédo, C.: An asymptotic sufficiency property of observations related to the first hitting times of a diffusion. Statistics & Probab. Letters. 9, 253-258 (1990)
8. Grama, I., and Nussbaum, M.: Asymptotic equivalence of nonparametric generalized linear models. Probab. Theory Relat. Fields 111, 167-214 (1998)
9. Jacod, J., and Shiryaev, A.: Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin, Heidelberg, New York (1987)
10. Jeganathan, P.: On the strong approximation of the distribution of estimators in linear stochastic models, I, II: Stationary and explosive AR models. Ann. Statist. 16, 1283-1314 (1988)
11. Kutoyants, Yu.A.: Parameter Estimation for Stochastic Processes. Heldermann, Berlin (1984)
12. Kutoyants, Yu.A.: On nonparametric estimation of trend coefficients in a diffusion process. In: Statistics and Control of Stochastic Processes, Steklov Seminar 1984 (Krylov, N. V., Liptser, R. Sh., Novikov, A. A. Eds.), Optimization Software. Inc, New York (1985)
13. Laredo, C.F.: A sufficient condition for asymptotic sufficiency of incomplete observations of a diffusion process. Ann. Statist. 18, 1158-1171 (1990)
14. Le Cam, L.: Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, Berlin, Heidelberg, New York (1986)
15. Le Cam, L., and Yang, G.: Asymptotics in Statistics. Springer-Verlag, Berlin, Heidelberg, New York (1990)
16. Liptser, R.S., and Shiryaev, A.: Statistics of Stochastic Processes. Springer-Verlag, Berlin, Heidelberg, New York (1977)
17. Nussbaum, M.: Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24, 2399-2430 (1996)
18. Øksendal, B.: Stochastic Differential Equations. Springer-Verlag, Berlin, Heidelberg, New York (1992)
19. Phillips, P.C.B.: Towards a unified asymptotic theory for autoregression. Biometrika 74, 535-547 (1987)
20. Shiryaev, A.N., and Spokoiny, V.: Statistical Experiments and Decisions: Asymptotic Theory. Unpublished manuscript
21. Stockmarr, A., and Jacobsen, M.: Gaussian diffusions and autoregressive processes: weak convergence and statistical inference. Scand. J. Statist. 21, 4 403-419 (1994)
22. Yoshida, N.: Estimation for diffusion processes from discrete observations. J. Multivariate Analysis 41, 220-242 (1992)