The International Journal of Biostatistics Score Statistics for Current Status Data : Comparisons with Likelihood Ratio and Wald Statistics
The International Journal of Biostatistics Score Statistics for Current Status Data : Comparisons with Likelihood Ratio and Wald Statistics
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发表时间：
2011
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通讯作者：
M. Banerjee
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作者：
M. Banerjee
在本文中，我们引入了三种自然的“分数统计”来检验F（t_0）在使用当前状态数据进行非参数推理的情况下取固定值的假设。这三个新的测试统计量在一定（加权）l2距离方面具有自然解释，并且也与自然的“片面”分数有关。我们将这些新的检验统计量与Banerjee和Wellner（2001）为同一检验问题引入的经典Wald统计量和似然比统计量的类比进行比较。在经典的“规则”统计问题下，似然比、分数和Wald统计量在零假设下都具有相同的楔形极限分布。与此形成鲜明对比的是，在这个非正则问题中，所有三种统计量在零假设下具有不同的极限分布。因此，我们首先建立了零假设下统计量的极限分布理论，并讨论了检验统计量的相关临界点的计算。一旦知道了零分布理论，直接的问题就变成了权力的问题。建立了三种统计量在局部替代条件下的极限行为。我们还通过一项有限的蒙特卡洛研究比较了这五种不同统计数据的效力。我们的结论是：(a) Wald统计量比似然比和评分统计量更弱；(b)对于某些选项，其中一个得分统计可能比似然比统计更有效。
In this paper we introduce three natural ``score statistics" for testing the hypothesis that F(t_0)takes on a fixed value in the context of nonparametric inference with current status data. These three new test statistics have natural interpretations in terms of certain (weighted) L_2 distances, and are also connected to natural ``one-sided" scores. We compare these new test statistics with the analogue of the classical Wald statistic and the likelihood ratio statistic introduced in Banerjee and Wellner (2001) for the same testing problem. Under classical ``regular" statistical problems the likelihood ratio, score, and Wald statistics all have the same chisquared limiting distribution under the null hypothesis. In sharp contrast, in this non-regular problem all three statistics have different limiting distributions under the null hypothesis. Thus we begin by establishing the limit distribution theory of the statistics under the null hypothesis, and discuss calculation of the relevant critical points for the test statistics. Once the null distribution theory is known, the immediate question becomes that of power. We establish the limiting behavior of the three types of statistics under local alternatives. We have also compared the power of these five different statistics via a limited Monte-Carlo study. Our conclusions are: (a) the Wald statistic is less powerful than the likelihood ratio and score statistics; and (b) one of the score statistics may have more power than the likelihood ratio statistic for some alternatives.