Scholarlink

<p>In practical applications, the issue of testing the high-dimensional coefficients of multiple response models is becoming increasingly important. Existing methods for testing the significance of high-dimensional multiple response models can handle only moderate feature dimensions <i>p</i> at most, but are inadequate when faced with feature dimensions far exceeding the sample size <i>n</i>. In this paper, we propose a testing procedure for the regression coefficients in multiple response regression models based on a multivariate U-statistic, which does not impose restrictions on the relative sizes of <i>n</i> and <i>p</i>. With the aid of the martingale central limit theorem, we demonstrate that the proposed statistic has an asymptotic multivariate normal distribution under mild assumptions. Based on the joint normal distribution, we construct a test statistic that fuses prior information through weights, but is heavily influenced by the weights. To address this issue, we introduce an ensemble testing procedure and prove its theoretical optimality in terms of Bahadur efficiency. Finally, numerical simulations and analysis of blood lipid data on the Erhualian pigs both indicate that the ensemble testing procedure exhibits higher powers and robustness compared with existing methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Ensemble testing for high-dimensional multiple response models

  • 期刊论文

  • 发表日期：

    2025年12月4日

查看全文
  • Xingwei Liu,
  • Wangli Xu,
  • Xu Guo

摘要

In practical applications, the issue of testing the high-dimensional coefficients of multiple response models is becoming increasingly important. Existing methods for testing the significance of high-dimensional multiple response models can handle only moderate feature dimensions p at most, but are inadequate when faced with feature dimensions far exceeding the sample size n. In this paper, we propose a testing procedure for the regression coefficients in multiple response regression models based on a multivariate U-statistic, which does not impose restrictions on the relative sizes of n and p. With the aid of the martingale central limit theorem, we demonstrate that the proposed statistic has an asymptotic multivariate normal distribution under mild assumptions. Based on the joint normal distribution, we construct a test statistic that fuses prior information through weights, but is heavily influenced by the weights. To address this issue, we introduce an ensemble testing procedure and prove its theoretical optimality in terms of Bahadur efficiency. Finally, numerical simulations and analysis of blood lipid data on the Erhualian pigs both indicate that the ensemble testing procedure exhibits higher powers and robustness compared with existing methods.