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<p>This paper considers a generalized nonparametric gamma kernel estimator for the regression function with nonnegative support. It is based on an incomplete sample, where the explanatory variable is observed, but some responses are missing randomly. The asymptotic properties of the proposed estimator are established under the assumption that the data are stationary and ergodic. This framework makes it possible to handle time series data, which are typically dependent. We establish the convergence rate of the estimator, both in probability and almost surely. In addition, its conditional bias, integrated mean square error, and asymptotic normality are derived. The choice of smoothing parameters is also discussed, as well as its application to conditional quantile estimation. A simulation study is conducted to compare the performance of the proposed estimator with other competitive estimators in finite samples. The estimator is applied to a real data set to impute missing responses.</p>

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Generalized nonparametric asymmetric kernel regression estimator with responses missing for nonnegative stationary and ergodic data

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Isma Debbah,
  • Naâmane Laïb,
  • Abdelkader Tatachak

摘要

This paper considers a generalized nonparametric gamma kernel estimator for the regression function with nonnegative support. It is based on an incomplete sample, where the explanatory variable is observed, but some responses are missing randomly. The asymptotic properties of the proposed estimator are established under the assumption that the data are stationary and ergodic. This framework makes it possible to handle time series data, which are typically dependent. We establish the convergence rate of the estimator, both in probability and almost surely. In addition, its conditional bias, integrated mean square error, and asymptotic normality are derived. The choice of smoothing parameters is also discussed, as well as its application to conditional quantile estimation. A simulation study is conducted to compare the performance of the proposed estimator with other competitive estimators in finite samples. The estimator is applied to a real data set to impute missing responses.