A class of local likelihood methods and near-parametric asymptotics
A class of local likelihood methods and near-parametric asymptotics
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DOI：
10.1111/1467-9868.00150
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发表时间：
1998-01-01
影响因子：
5.8
通讯作者：
Copas, J
中科院分区：
文献类型：
--
作者：
Eguchi, S;Copas, J
统计模型f（x，theta）中参数的局部最大似然估计（t）是通过最大化似然函数的加权版本来定义的，该加权版本为t附近的观测值提供更多权重。本文研究了f（t，（t））比通常的估计f（t，）更接近真实分布g（t）的意义。渐近结果的情况下，模型的误设定变得消失的小样本大小趋于无穷大。在这种情况下，局部方法的相对熵风险优于最大似然法。对于正态分布，得到了局部似然的最优权的形式，并举例说明。
The local maximum likelihood estimate (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, (t)) is closer to the true distribution g(t) than the usual estimate f(t, ) 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.