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We propose a non-parametric higher order asymptotic unbiased estimator of residual variance in the varying coefficient regression model with q smoothing variables. The estimation method is based on a local linear fitting and does not require optimization of hyperparameters such as the bandwidth of the kernel function or the smoothing parameters of the penalized smoothing spline. The order of the bias of the proposed estimator is \(O(n^{-4/q})\) under appropriate conditions.

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Non-parametric Bias-Reduction Estimation of Residual Variance in Varying Coefficient Regression Model

  • 会议论文

  • 发表日期：

    2025年

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  • Hirokazu Yanagihara,
  • Sanai Shibayama

摘要

We propose a non-parametric higher order asymptotic unbiased estimator of residual variance in the varying coefficient regression model with q smoothing variables. The estimation method is based on a local linear fitting and does not require optimization of hyperparameters such as the bandwidth of the kernel function or the smoothing parameters of the penalized smoothing spline. The order of the bias of the proposed estimator is \(O(n^{-4/q})\) under appropriate conditions.