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<p>Measurement errors are always inevitable in many data collection procedures. Despite the fundamental role of degrees of freedom in statistics, its behavior when measurement errors exist is not well understood. In this paper, we propose an unbiased and consistent estimator of the degrees of freedom to measure the model complexity when the data has repeated covariate measurement errors. Based on the estimated degrees of freedom, we propose a model selection criterion. The selection procedure based on the proposed criterion can achieve asymptotic loss efficiency and selection consistency with a more relaxed condition. Comprehensive simulation studies demonstrate the asymptotic properties of the proposed approach. We apply the proposed selection procedure to obesity data. The proposed approach achieves good prediction performance with more parsimonious models.</p>

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Degrees of Freedom and Model Selection in Linear Models with Repeated Measurement Errors

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Caihong Qin,
  • Mengli Zhang,
  • Huichen Zhu,
  • Yang Bai

摘要

Measurement errors are always inevitable in many data collection procedures. Despite the fundamental role of degrees of freedom in statistics, its behavior when measurement errors exist is not well understood. In this paper, we propose an unbiased and consistent estimator of the degrees of freedom to measure the model complexity when the data has repeated covariate measurement errors. Based on the estimated degrees of freedom, we propose a model selection criterion. The selection procedure based on the proposed criterion can achieve asymptotic loss efficiency and selection consistency with a more relaxed condition. Comprehensive simulation studies demonstrate the asymptotic properties of the proposed approach. We apply the proposed selection procedure to obesity data. The proposed approach achieves good prediction performance with more parsimonious models.