Hellinger Deviance Tests: Efficiency, Breakdown Points, and Examples
Hellinger 偏差检验：效率、崩溃点与实例AI 解读 ↓
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Hellinger 偏差检验：效率、崩溃点与实例
- 研究问题
- 如何构造对异常观测更稳健的参数假设检验，同时在模型正确时保留似然比检验的渐近效率特征？
- 方法与思路
- 作者以非参数密度估计分别到零假设和无约束参数模型的最小 Hellinger 距离构造检验，并比较崩溃性质。
- 材料陈述的贡献
- 摘要称，模型正确时该检验与似然比检验渐近等价，通常具有较高崩溃点，并用模拟和两个实例评价有限样本表现。
- 阅读关注点
- 核对密度估计与平滑选择、渐近等价的正则条件，以及检验崩溃点的定义和污染情形下的功效表现。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；高崩溃点与渐近等价均需具体条件，摘要未给出有限样本比较数值，不能断言普遍更优。
原文摘要
Hellinger distance analogs of likelihood ratio tests are proposed for parametric inference. The proposed tests are based on minimized Hellinger distances between nonparametric density estimates and densities corresponding to null and unconstrained parametric models. If the parametric model is correct, the Hellinger deviance test is asymptotically equivalent to the likelihood ratio test. A simulation study examines the relative performance of these tests in finite samples. Breakdown properties of the Hellinger deviance tests and likelihood ratio tests are compared. The Hellinger tests are generally high breakdown-point tests, whereas, in many instances, the likelihood ratio tests have breakdown points of 0. Two numerical examples illustrate the implementation and performance of the proposed tests. Likelihood-based methods are widely used in applications. They provide a routine method for generating efficient estimates and inference statements. In many instances, however, these methods are known to be sensitive to anomalous data points, and the careful data analyst will screen for outliers prior to a likelihood-based analysis. In large-scale data analysis, for instance, when processing the results of many similar experiments in a data base, the outlier screening procedure needs to be automated. This type of data processing is common in mutation research, where numerous chemicals are subjected to a battery of mutagenicity and carcinogenicity trials. An automated outlier screen is one method for obtaining robust inferences in this setting. The Hellinger test studied here is proposed as a more direct method for obtaining robust inferences. The test statistic simply measures how much farther the data are from the null model than from the unconstrained model. Regions of low predicted density receive very little weight, so the Hellinger deviance test is able to cope with anomalous data. The method adapts to a variety of parametric hypothesis testing situations.