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首页> 外文期刊>Journal of applied statistics >Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density
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Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density

机译：未知误差密度功能部分线性模型的贝叶斯带宽估计和半标题选择

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摘要

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.
机译：本研究检查了功能部分线性模型的带宽和半标的最佳选择。我们所提出的方法通过使用残差的核密度估计来估计未知的误差密度，其中可以通过功能主组件和功能Nadayara-Watson估计来估计由参数和非参数分量组成的回归函数。回归函数的估计准确性和误差密度至关重要，这取决于带宽和半指标的最佳估计。通过最小化Kullback-Leibler发散，贝叶斯方法用于同时估计回归函数和内核误差密度的带宽。为了估计回归函数和误差密度，一系列仿真研究表明，与功能主成分回归和功能非参数回归相比，功能部分线性模型可提高估计和预测精度。使用光谱数据集，功能部分线性模型会产生比某些常用的功能回归模型更好的预测精度。作为贝叶斯方法的副产物，可以获得尖预测的间隔，并且可以使用边缘似然来选择最佳的半标目。

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