A Second-order Adjustment to the Profile Likelihood in the Case of a Multidimensional Parameter of Interest
多维目标参数情形下剖面似然的二阶调整AI 解读 ↓
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多维目标参数情形下剖面似然的二阶调整
- 研究问题
- 存在干扰参数且目标参数为多维向量时，如何修正剖面似然的得分与信息偏差，改善小样本中似然比推断的可靠性？
- 方法与思路
- 作者提出新的加性调整函数，使调整后的剖面似然降低得分和信息偏差，并能应用于包含向量目标参数的一般参数框架。
- 材料陈述的贡献
- 摘要称新调整克服已有方法对特定参数框架的依赖，适用于多维目标参数，并通过例子比较小样本推断表现。
- 阅读关注点
- 阅读全文时应核对调整项的计算方式、二阶性质的准确含义、正则条件，以及小样本比较采用的误差指标。
- 阅读边界
- 仅据所给 Crossref 摘要，调整公式与误差阶未说明；降低得分和信息偏差并不直接保证所有置信域覆盖率更好。
原文摘要
Summary Inference in the presence of nuisance parameters is often carried out by using the χ2-approximation to the profile likelihood ratio statistic. However, in small samples, the accuracy of such procedures may be poor, in part because the profile likelihood does not behave as a true likelihood, in particular having a profile score bias and information bias which do not vanish. To account better for nuisance parameters, various researchers have suggested that inference be based on an additively adjusted version of the profile likelihood function. Each of these adjustments to the profile likelihood generally has the effect of reducing the bias of the associated profile score statistic. However, these adjustments are not applicable outside the specific parametric framework for which they were developed. In particular, it is often difficult or even impossible to apply them where the parameter about which inference is desired is multidimensional. In this paper, we propose a new adjustment function which leads to an adjusted profile likelihood having reduced score and information biases and is readily applicable to a general parametric framework, including the case of vector-valued parameters of interest. Examples are given to examine the performance of the new adjusted profile likelihood in small samples, and also to compare its performance with other adjusted profile likelihoods.