作者：Aeckerle-willems, Cathrine; Strauch, Claudia
作者单位：University of Mannheim; Aarhus University
摘要：We consider the question of estimating the drift for a large class of er-godic multivariate and possibly nonreversible diffusion processes, based on continuous observations, in sup-norm loss. Nonparametric classes of smooth functions of unknown order are considered, and we suggest an adaptive ap-proach which allows to construct drift estimators attaining optimal sup-norm rates of convergence. Reversibility structures and related functional inequali-ties are known to be key tools for these esti...
作者：Heiny, Johannes; Yao, Jianfeng
作者单位：Ruhr University Bochum; The Chinese University of Hong Kong, Shenzhen
摘要：Consider a p-dimensional population x is an element of R-p with i.i.d. coordinates that are regularly varying with index alpha is an element of(0, 2). Since the variance of x is infinite, the diagonal elements of the sample covariance matrix S-n = n(-1) Sigma(n)(i=1) x(i)x(i)' based on a sample x(1), . . . , x(n) from the population tend to infinity as n increases and it is of interest to use instead the sample correlation matrix R-n = {diag(S-n)}S--1/2(n){diag(S-n)}(-1/2). This paper finds th...
