An evaluation of the power and conditionality properties of empirical likelihood
经验似然的功效与条件性性质评估AI 解读 ↓
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经验似然的功效与条件性性质评估
- 研究问题
- 经验似然和对偶似然相对普通参数似然，在标量参数检验的局部功效及条件推断性质上有何差异？
- 方法与思路
- 作者以二阶、三阶局部功效比较人工似然与真实似然，并通过与准似然比较，考察不同离散程度设定下的条件性性质。
- 材料陈述的贡献
- 摘要称二阶比较中没有效率损失；三阶优劣取决于信息、假设距离及模型曲率，条件推断的选择还取决于离散程度是否已知。
- 阅读关注点
- 应核对局部备择的设定、展开阶数与效率定义，以及辅助统计量的构造和离散程度已知时采用准似然的具体依据。
- 阅读边界
- 仅据稿件版本未注明的OpenAlex索引摘要；正则条件和证明未提供，不能将二阶结论扩展为经验似然普遍优于参数似然。
原文摘要
Empirical and dual likelihood are two of a growing array of artificial or approximate likelihoods currently in use in statistics. A question of major interest focuses on the performance of these new constructs relative to ordinary parametric likelihoods. We consider here two criteria, local power and conditional properties. Looking at tests of a scalar parameter, we show that there is no loss of efficiency in using a dual or empirical likelihood model, to second order. To third order, either the artificial likelihood or the true likelihood test could be more efficient; this is determined by the Fisher information, the distance between the null and the alternative hypotheses, and the statistical curvature of the models. Conditionality properties are assessed by comparing empirical likelihood with quasilikelihood. If there is overdispersion present, or more generally an unknown amount of dispersion, then there is little difference in the ancillaries for conditional inference based on empirical likelihood or on other possible likelihoods, such as a quasilikelihood. If the amount of dispersion is known, however, it is correct to base inference on the quasilikelihood.