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<p>We study a score statistic for inference on an interest parameter in a linear model with omitted covariates, establishing Berry–Esseen and Cramér-type moderate deviation bounds on the associated normal approximation. This entails a coupling between well-behaved but unobservable random variables and observable ones to which standard results do not straightforwardly apply. The theory is of self-standing interest but also provides new insights on backwards reduction procedures used in high-dimensional regression. An example details how our results may be used to analyse the high-dimensional procedure proposed by Cox and Battey (<i>Proceedings of the National Academy of Sciences,</i> <b>114</b>, 8592–8595, 2017).</p>

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Inference in models with omitted covariates: Cramér-type moderate deviations and applications to high-dimensional regression

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Rebecca M. Lewis,
  • Heather S. Battey,
  • Wen-Xin Zhou

摘要

We study a score statistic for inference on an interest parameter in a linear model with omitted covariates, establishing Berry–Esseen and Cramér-type moderate deviation bounds on the associated normal approximation. This entails a coupling between well-behaved but unobservable random variables and observable ones to which standard results do not straightforwardly apply. The theory is of self-standing interest but also provides new insights on backwards reduction procedures used in high-dimensional regression. An example details how our results may be used to analyse the high-dimensional procedure proposed by Cox and Battey (Proceedings of the National Academy of Sciences, 114, 8592–8595, 2017).