论文标题
具有未知误差密度的功能部分线性模型的贝叶斯带宽估计和半度选择
Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density
论文作者
论文摘要
这项研究研究了功能部分线性模型的带宽和半米度的最佳选择。我们提出的方法首先使用残留物的核密度估计器估算未知的误差密度，在该核心密度估计器中，可以通过功能主组件和功能性Nadayara-Watson估计器来估算由参数和非参数组件组成的回归函数。回归函数和误差密度的估计准确性至关重要取决于带宽和半米度的最佳估计。通过最小化kullback-leibler差异，一种贝叶斯方法用于同时估计回归函数和内核误差密度中的带宽。为了估计回归函数和误差密度，一系列仿真研究表明，与功能性主组件回归和功能性非参数回归相比，功能性部分线性模型可改善估计和预测精度。使用光谱数据集，功能性部分线性模型比某些常用的功能回归模型得出的预测精度更好。作为贝叶斯方法的副产品，可以获得一个侧面的预测间隔，并且可以使用边缘可能性来选择最佳的半度尺度。
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.
