Inference on multiple correlation coefficients with moderately high dimensional data

• 成果类型: Article
• 署名作者: Zheng, Shurong; Jiang, Dandan; Bai, Zhidong; He, Xuming
• 署名单位: Northeast Normal University - China; Jilin University; University of Michigan System; University of Michigan
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu023
• 发表日期: 2014
• 页码: 748754
• 关键词: square; series; tests

摘要

When the multiple correlation coefficient is used to measure how strongly a given variable can be linearly associated with a set of covariates, it suffers from an upward bias that cannot be ignored in the presence of a moderately high dimensional covariate. Under an independent component model, we derive an asymptotic approximation to the distribution of the squared multiple correlation coefficient that depends on a simple correction factor. We show that this approximation enables us to construct reliable confidence intervals on the population coefficient even when the ratio of the dimension to the sample size is close to unity and the variables are non-Gaussian.