ON THE ASYMPTOTICS OF CONSTRAINED M-ESTIMATION
成果类型：
Article
署名作者：
GEYER, CJ
署名单位：
University of Chicago
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176325768
发表日期：
1994
页码：
1993-2010
关键词：
摘要：
Limit theorems for an M-estimate constrained to lie in a closed subset of R(d), given under two different sets of regularity conditions. A consistent sequence of global optimizers converges under Chernoff regularity of the parameter set. A root n-consistent sequence of local optimizers converges under Clarke regularity of the parameter set. In either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value. Limit theorems for the optimal value are also obtained, agreeing with Chernoff's result in the case of maximum likelihood with global optimizers.