A class of local likelihood methods and near-parametric asymptotics
成果类型：
Article
署名作者：
Eguchi, S; Copas, J
署名单位：
University of Warwick; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1111/1467-9868.00150
发表日期：
1998
页码：
709-724
关键词：
摘要：
The local maximum likelihood estimate <(theta)over cap>(t) of a parameter in a statistical model f(x, theta) is defined by maximizing a weighted version of the likelihood function which gives more weight to observations in the neighbourhood of t. The paper studies the sense in which f(t, <(theta)over cap>(t)) is closer to the true distribution g(t) than the usual estimate f(t, <(theta)over cap>) is. Asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the sample size tends to infinity. In this setting, the relative entropy risk of the local method is better than that of maximum likelihood. The form of optimum weights for the local likelihood is obtained and illustrated for the normal distribution.
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