论文标题
非参数回归模型中局部线性拟合的贝叶斯带宽估计
Bayesian bandwidth estimation for local linear fitting in nonparametric regression models
论文作者
论文摘要
本文提出了一种在非参数回归模型中回归函数的局部线性估计器的带宽估计方法的贝叶斯采样方法。在贝叶斯采样方法中，误差密度通过高斯密度的位置混合密度近似，该密度是指单个误差和方差恒定参数。该混合物密度具有误差的核密度估计量的形式，称为内核形式误差密度（C.F.，Zhang等，2014）。而Zhang等人。 （2014年）使用局部常数（也称为Nadaraya-Watson）估计器来估计回归函数，我们将其扩展到局部线性估计器，从而产生更准确的估计。所提出的研究是由于缺乏数据驱动的方法用于在回归函数和内核形式误差密度的局部线性估计器中同时选择带宽。将带宽视为参数，我们得出了近似（伪）的可能性和后部。一项仿真研究表明，在集成平方误差的标准下，提出的带宽估计优于脑规则和交叉验证方法。提出的带宽估计方法通过涉及企业所有权集中的非参数回归模型以及涉及国家价格密度估计的模型来验证。
This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by a location-mixture density of Gaussian densities with means the individual errors and variance a constant parameter. This mixture density has the form of a kernel density estimator of errors and is referred to as the kernel-form error density (c.f., Zhang et al., 2014). While Zhang et al. (2014) use the local constant (also known as the Nadaraya- Watson) estimator to estimate the regression function, we extend this to the local linear estimator, which produces more accurate estimation. The proposed investigation is motivated by the lack of data-driven methods for simultaneously choosing bandwidths in the local linear estimator of the regression function and kernel-form error density. Treating bandwidths as parameters, we derive an approximate (pseudo) likelihood and a posterior. A simulation study shows that the proposed bandwidth estimation outperforms the rule-of-thumb and cross-validation methods under the criterion of integrated squared errors. The proposed bandwidth estimation method is validated through a nonparametric regression model involving firm ownership concentration, and a model involving state-price density estimation.
