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| Wald检验不一致性的微分几何解释及改进 | |
| 引用本文： | 王泽锋,郭迎弟. Wald检验不一致性的微分几何解释及改进[J]. 统计与信息论坛, 2007, 22(5): 18-21 |
| 作者姓名： | 王泽锋 郭迎弟 |
| 作者单位： | 1. 西南财经大学,统计学院,四川,成都,610074 2. 西南大学,数学与统计学院,四川,成都,400715 |
| 摘 要： | Wald检验对于等价的零假设中不同形式的表达式在有限样本的情况下缺乏一致性,而从微分几何的角度来解释这一现象,并发现由于Wald统计量是一个混杂的不恰当的几何量,从而对不同的含参数的等价表达式不具有一致性。同时还展示了芬斯拉（Finsler）测地统计量如何能较为简便的计算出来、它在线性回归模型中的非线性约束条件下如何应用以及两者在什么情况下保持一致,并提出了一种解决Wald检验不一致性的思路。 |
| 关 键 词： | WALD检验 芬斯拉测地统计量 流形 |
| 文章编号： | 1007-3116(2007)05-0018-04 |
| 修稿时间： | 2007-05-21 |
An Explanation and Improvement on the Invariance of the Wald Test on the Differential Geometry |
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| WANG Ze-feng,GUO Ying-di. An Explanation and Improvement on the Invariance of the Wald Test on the Differential Geometry[J]. Statistics & Information Tribune, 2007, 22(5): 18-21 | |
| Authors: | WANG Ze-feng GUO Ying-di |
| Affiliation: | WANG Ze-feng, GUO Ying-di (1. School of Statistics, Southwest University of Finance and Economics, Chengdu 610074, China; 2. School of Mathematics and Statistics, Xi＇nan University, Chengdu 610074, China) |
| Abstract: | In this paper,we exploit the tools of differential geometry to provide an explanation for the finite sample lack of invariance of the Wald statistic to algebraically equivalent reformulations of the null hypothesis and find that the Wald statistic is shown,in general,to be an improper geometric quantity and hence is not invariant to reparameterizations.Also,we show how this "Finsler geodesic statistic" may be easily calculated.It is applied in the case of testing nonlinear restrictions in the linear model and when it will coincide with the Wald statistic.At the end,we provide a new method to improve the lack of invariance of the Wald statistic. |
| Keywords: | Wald test Finsler geodesic statistic manifold |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |