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<p>High-dimensional data with measurement errors pose significant challenges for statistical modeling and inference due to the “curse of dimensionality” and the unavailability of direct measurements of variables. To reduce the dimensionality of data, feature screening is an effective method for identifying informative variables among a large number of observed features. While feature screening has been extensively studied in the literature, limited research has focused on feature screening with random variables affected by measurement errors. In this paper, we propose an adjusted martingale difference correlation (AMDC) to measure conditional mean dependence in the presence of measurement errors. We further extend the proposed AMDC to measure the dependence of the conditional quantile and conditional <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textit{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">k</mi> </math></EquationSource> </InlineEquation>th central moment through specific transformations of the error-prone variables. We establish invariance relationships between the AMDC and the original martingale difference correlation and develop different feature screening methods for the conditional mean, conditional quantile, and conditional <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textit{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">k</mi> </math></EquationSource> </InlineEquation>th central moment of the response variable under a measurement error model. We establish sure screening properties for all the proposed procedures and conduct extensive simulation studies to illustrate their effectiveness and advantages. Finally, we analyze microRNA expression data using the proposed AMDC-based screening methods to demonstrate their practical usefulness.</p>

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Feature Screening for High-Dimensional Data with Measurement Errors using Adjusted Martingale Difference Correlation

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Wei Liu,
  • Wenbo Wu,
  • Baoying Yang

摘要

High-dimensional data with measurement errors pose significant challenges for statistical modeling and inference due to the “curse of dimensionality” and the unavailability of direct measurements of variables. To reduce the dimensionality of data, feature screening is an effective method for identifying informative variables among a large number of observed features. While feature screening has been extensively studied in the literature, limited research has focused on feature screening with random variables affected by measurement errors. In this paper, we propose an adjusted martingale difference correlation (AMDC) to measure conditional mean dependence in the presence of measurement errors. We further extend the proposed AMDC to measure the dependence of the conditional quantile and conditional \(\textit{k}\) k th central moment through specific transformations of the error-prone variables. We establish invariance relationships between the AMDC and the original martingale difference correlation and develop different feature screening methods for the conditional mean, conditional quantile, and conditional \(\textit{k}\) k th central moment of the response variable under a measurement error model. We establish sure screening properties for all the proposed procedures and conduct extensive simulation studies to illustrate their effectiveness and advantages. Finally, we analyze microRNA expression data using the proposed AMDC-based screening methods to demonstrate their practical usefulness.