Tests for High-Dimensional Regression Coefficients With Factorial Designs

• 成果类型: Article
• 署名作者: Zhong, Ping-Shou; Chen, Song Xi
• 署名单位: Iowa State University; Peking University; Peking University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.tm10284
• 发表日期: 2011
• 页码: 260-274
• 关键词: Nonparametric methods; expression profiles; asymptotic-behavior; microarray data; large number; M-ESTIMATORS; rank-tests; selection; parameters; anova

摘要

We propose simultaneous tests for coefficients in high-dimensional linear regression models with factorial designs. The proposed tests are designed for the large p, small n situations where the conventional F-test is no longer applicable. We derive the asymptotic distribution of the proposed test statistic under the high-dimensional null hypothesis and various scenarios of the alternatives, which allow power evaluations. We also evaluate the power of the F-test for models of moderate dimension. The proposed tests are employed to analyze a microarray data on Yorkshire Gilts to find significant gene ontology terms which are significantly associated with the thyroid hormone after accounting for the designs of the experiment.