论文标题
概率质量函数的归一化离散 - 内核估计量的渐近特性
Asymptotic properties of the normalized discrete associated-kernel estimator for probability mass function
论文作者
论文摘要
离散的内核平滑现在在非参数统计中变得重要。在本文中，我们研究了概率质量函数的标准化离散相关内核估计器的一些渐近特性。我们在相关的内分子上表明，在某些规律性和非限制性假设下，归一化的随机变量在均值中收敛至1。然后，我们得出了所提出的估计量的一致性和渐近正态性。各种离散核的家族已经表现出满足条件，包括不足和二阶的精制Com-Poisson。最后，讨论了一阶二项式内核，令人惊讶的是，其归一化估计量通过模拟具有合适的渐近行为。
Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalized discrete associated-kernel estimator of a probability mass function. We show, under some regularity and non-restrictive assumptions on the associated-kernel, that the normalizing random variable converges in mean square to 1. We then derive the consistency and the asymptotic normality of the proposed estimator. Various families of discrete kernels already exhibited satisfy the conditions, including the refined CoM-Poisson which is underdispersed and of second-order. Finally, the first-order binomial kernel is discussed and, surprisingly, its normalized estimator has a suitable asymptotic behaviour through simulations.
