Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a class of estimators, consistent simultanously for both a semiparametric distribution and a distinct parametric distribution, is proposed. These efficient estimators are robust to both gross errors and departures from parametric assumptions, making them ideal for estimating the mean and central moments of common unimodal distributions. This article opens up the possibility of utilizing the common nature of probability models to construct near-optimal estimators that are suitable for various scenarios.

翻译：参数模型的描述性统计目前对偏离、粗大误差和/或随机误差高度敏感。本文利用参数分布及其中心矩核分布的结构，提出了一类同时适用于半参数分布与特定参数分布的一致估计量。这些高效估计量对粗大误差及参数假设偏离均具有稳健性，使其成为估计常见单峰分布均值与中心矩的理想工具。本文揭示了利用概率模型共性构建适用于多种场景的近似最优估计量的可能性。