A van Trees inequality for estimators on manifolds

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Jupp, P. E.

关键词: Bayes risk;    Bias;    Cramer-Rao inequality;    Fisher information;    Hessian;    Proper dispersion model;    Tensor;   

DOI  :  10.1016/j.jmva.2010.03.007

来源: Elsevier

【 摘 要 】

Van Trees' Bayesian version of the Cramer-Rao inequality is generalised here to the context of smooth loss functions on manifolds and estimation of parameters of interest. This extends the multivariate van Trees inequality of Gill and Levit (1995) [R.D. Gill, B.Y. Levit, Applications of the van Trees inequality: a Bayesian Cramer-Rao bound, Bernoulli 1 (1995) 59-79]. In addition, the intrinsic Cramer-Rao inequality of Hendriks (1991) [H. Hendriks, A Cramer-Rao type lower bound for estimators with values in a manifold, J. Multivariate Anal. 38 (1991) 245-261] is extended to cover estimators which may be biased. The quantities used in the new inequalities are described in differential-geometric terms. Some examples are given. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free