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<p>In this paper, we propose a local polynomial modal regression framework to study the relationship between a response variable and a covariate subject to Laplace measurement error. The estimation procedure relies on a bias-corrected nonparametric kernel estimator of the joint density of the covariate and the modal regression residual, constructed via a polynomial approximation of the modal regression function. Theoretical results establish that the proposed estimator possesses desirable asymptotic properties, including consistency and asymptotic normality. Comprehensive simulation studies further demonstrate that our method consistently outperforms existing alternatives. Finally, we illustrate the practical applicability of the approach through a real data example.</p>

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Nonparametric Modal Regression with Laplace Measurement Error

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Yanfei He,
  • Jianhong Shi,
  • Weixing Song

摘要

In this paper, we propose a local polynomial modal regression framework to study the relationship between a response variable and a covariate subject to Laplace measurement error. The estimation procedure relies on a bias-corrected nonparametric kernel estimator of the joint density of the covariate and the modal regression residual, constructed via a polynomial approximation of the modal regression function. Theoretical results establish that the proposed estimator possesses desirable asymptotic properties, including consistency and asymptotic normality. Comprehensive simulation studies further demonstrate that our method consistently outperforms existing alternatives. Finally, we illustrate the practical applicability of the approach through a real data example.