Scholarlink

<p>We propose a robust projection-based test to check linear regression models when the dimension may be divergent. The proposed test can maintain the type I error rate effectively when outliers are present, achieve dimension reduction as if only a single covariate was present, and inherited the robustness of the M-estimation. The test is shown to be consistent and can detect root-<i>n</i> local alternative hypotheses. We further derive asymptotic distributions of the proposed test under the null hypothesis and analyze asymptotic properties under the local and global alternatives. We evaluate the finite-sample performance via simulation studies and apply the proposed method to analyze a real dataset as an illustration.</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

A Robust Projection-Based Test for Goodness-of-Fit in Linear Models with a Divergent Number of Covariates

  • 期刊论文

  • 发表日期：

    2026年3月27日

查看全文
  • Xiao Wang,
  • Xinmin Li,
  • Yu Xia,
  • Hua Liang

摘要

We propose a robust projection-based test to check linear regression models when the dimension may be divergent. The proposed test can maintain the type I error rate effectively when outliers are present, achieve dimension reduction as if only a single covariate was present, and inherited the robustness of the M-estimation. The test is shown to be consistent and can detect root-n local alternative hypotheses. We further derive asymptotic distributions of the proposed test under the null hypothesis and analyze asymptotic properties under the local and global alternatives. We evaluate the finite-sample performance via simulation studies and apply the proposed method to analyze a real dataset as an illustration.