Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters by the maximum likelihood and weighted score methods.
Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters by the maximum likelihood and weighted score methods.
复制标题
通过最大似然和加权评分方法对拉格朗日乘子和相关参数的估计量进行渐近展开。
DOI：
10.1016/j.jmva.2015.12.015
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发表时间：
2016
影响因子：
1.6
通讯作者：
H.
中科院分区：
文献类型：
--
作者：
Ogasawara;H.
本文给出了参数估计的真值逆展开式，其中参数估计由极大似然法和加权评分法得到，参数的约束条件由拉格朗日乘子给出.并给出了相应的估计拉格朗日乘子的展开式。这些扩展是在学生化之前和之后得出的。学生化的结果给出了单侧置信区间的参数高达三阶精度。作为加权得分法的应用，在指数族的正则参数化下，得到了一个修正的Jeffreys先验，消除了拉格朗日乘子和参数估计的渐近偏差.
In this paper, inverse expansions of parameter estimators are given in terms of their true values, where the estimators are obtained by the maximum likelihood and weighted score methods with constraints placed on the parameters using Lagrange multipliers. The corresponding expansions for estimated Lagrange multipliers are also given. These expansions are derived before and after studentization. The results with studentization give one-sided confidence intervals for the parameters up to third-order accuracy. As an application of the weighted score method, a modified Jeffreys prior to remove the asymptotic biases of the Lagrange multipliers as well as the parameter estimators is obtained under canonical parametrization in the exponential family.