论文标题
具有贝叶斯自适应带宽的非负数据的多个组合伽马内核估计
Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths
论文作者
论文摘要
修改后的伽马内核不应自动优先于标准的伽马内核，尤其是对于单变量的凸透密度，其原点是极点。在多变量情况下，在这里引入了多个被定义为单变量标准和修改后的产品的组合伽马内核，用于非参数和半摩托平滑，对未知的矫正密度具有支持$ [0，\ infty）^d $。建立了这些相关核估计器的渐近性能。使用多个纯联合γ型Smoothors以及在半参数设置中，贝叶斯对自适应带宽矢量的估计是在通常的二次函数下精确得出的。真实数据集上的仿真结果和四个插图揭示了提出的非参数平滑方法的组合方法非常有趣，与纯标准和纯修改的伽马内核版本进行了比较，以及在集成的平方误差和平均日志性误差标准下。
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a product of univariate standard and modified ones, are here introduced for nonparametric and semiparametric smoothing of unknown orthant densities with support $[0,\infty)^d$. Asymptotical properties of these multivariate associated kernel estimators are established. Bayesian estimation of adaptive bandwidth vectors using multiple pure combined gamma smoothers, and in semiparametric setup, are exactly derived under the usual quadratic function. The simulation results and four illustrations on real datasets reveal very interesting advantages of the proposed combined approach for nonparametric smoothing, compare to both pure standard and pure modified gamma kernel versions, and under integrated squared error and average log-likelihood criteria.
