采用贝叶斯自适应带宽的非负数据多重组合 gamma 核估计
Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths
AI总结：
针对支撑于非负正交限的多变量密度，本文提出标准与修正 gamma 核的多重组合估计及贝叶斯自适应带宽选择，证明其渐近性质，并通过仿真和真实数据显示优于两类纯核方法。
摘要：
修正 gamma 核不应被自动优先于标准 gamma 核，尤其是对于在原点处存在极点的单变量凸密度而言。在多变量情形下，本文引入多重组合 gamma 核，将其定义为单变量标准核与修正核的乘积，用于对支撑集为 $[0,\infty)^d$ 的未知正交限密度进行非参数和半参数平滑。文中建立了这些多变量关联核估计量的渐近性质。在通常的二次函数下，精确推导了使用多重纯组合 gamma 平滑器以及在半参数设定中对自适应带宽向量进行贝叶斯估计的方法。仿真结果和四个真实数据集示例表明，在积分平方误差和平均对数似然准则下，与纯标准和纯修正 gamma 核版本相比，所提出的组合方法在非参数平滑方面具有非常引人关注的优势。
英文摘要：
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.
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