LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS
LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS
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DOI：
10.1214/18-aos1761
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发表时间：
2019-10-01
影响因子：
4.5
通讯作者：
Li, Runze
中科院分区：
文献类型：
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作者：
Shi, Chengchun;Song, Rui;Li, Runze
研究了高维广义线性模型中线性假设的检验问题。为了处理线性假设，我们首先提出了约束部分正则化方法，并研究了它的统计性质。我们进一步介绍了一个算法，用于解决正则化问题的折叠凹罚函数和线性约束。为了检验线性假设，我们提出了部分惩罚似然比检验，部分惩罚分数检验和部分惩罚Wald检验。我们证明了这三个检验统计量的极限零分布都是具有相同自由度的chi（2）分布，并且在局部替代下，只要检验假设中涉及的参数个数以一定的速率增长到无穷大，它们渐近服从具有相同自由度和非中心参数的非中心chi（2）分布.进行模拟研究，以检查所提出的测试的有限样本性能。一个真实的数据的实证分析被用来说明所提出的测试程序。
This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are chi(2) distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow noncentral chi(2) distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to infinity at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.