Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case

被引：0
作者：
Arnak Dalalyan
Markus Reiß
机构：
[1] Université Paris VI,Laboratoire de Probabilités
[2] University of Heidelberg,Institute of Applied Mathematics
来源：
Probability Theory and Related Fields | 2007年 / 137卷
关键词：
62B15; 62G05; 62G07; 62G20; 62M05; Asymptotic equivalence; Statistical experiment; Le Cam distance; Ergodic diffusion; Gaussian shift; Heteroskedastic regression;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Asymptotic local equivalence in the sense of Le Cam is established for inference on the drift in multidimensional ergodic diffusions and an accompanying sequence of Gaussian shift experiments. The nonparametric local neighbourhoods can be attained for any dimension, provided the regularity of the drift is sufficiently large. In addition, a heteroskedastic Gaussian regression experiment is given, which is also locally asymptotically equivalent and which does not depend on the centre of localisation. For one direction of the equivalence an explicit Markov kernel is constructed.
引用
收藏
页码：25 / 47
页数：22
相关论文
共 29 条
[1]  
Bhattacharya R. N.(1978)Criteria for recurrence and existence of invariant measures for multidimensional diffusions Ann. Probab. 6 541-553
[2]  
Brown L. D.(2002)Asymptotic equivalence theory for nonparametric regression with random design. Dedicated to the memory of Lucien Le Cam Ann. Statist. 30 688-707
[3]  
Cai T. T.(1996)Asymptotic equivalence of nonparametric regression and white noise Ann. Stat. 24 2384-2398
[4]  
Low M. G.(1998)Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2 Ann. Stat. 26 279-287
[5]  
Zhang C.-H.(2006)A continuous Gaussian process approximation to a nonparametric regression in two dimensions Bernoulli 12 143-156
[6]  
Brown L. D.(1986)On smoothed probability density estimation for stationary processes Stochastic Process. Appl. 21 179-193
[7]  
Low M. G.(1997)Estimation of spectral gap for elliptic operators Trans. Amer. Math. Soc. 349 1239-1267
[8]  
Brown L. D.(2006)Asymptotic statistical equivalence for scalar ergodic diffusions Probab. Theory Rel. Fields 134 248-282
[9]  
Zhang C.(2002)Asymptotic equivalence for a null recurrent diffusion Bernoulli 8 139-174
[10]  
Carter A. V.(2004)Weighted uniform consistency of kernel density estimators Ann. Prob. 32 2570-2605
123