The density function is a fundamental concept in data analysis. When a population consists of heterogeneous subjects, it is often of great interest to estimate the density functions of the subpopulations. Nonparametric methods such as kernel smoothing estimates may be applied to each subpopulation to estimate the density functions if there are no missing values. In situations where the membership for a subpopulation is missing, kernel smoothing estimates using only subjects with membership available are valid only under missing complete at random (MCAR). In this paper, we propose new kernel smoothing methods for density function estimates by applying prediction models of the membership under the missing at random (MAR) assumption. The asymptotic properties of the new estimates are developed, and simulation studies and a real study in mental health are used to illustrate the performance of the new estimates.

中文翻译：

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当组成员身份容易丢失时，基于预测模型的内核密度估计。

密度函数是数据分析中的基本概念。当种群由异质主体组成时，估计亚种群的密度函数通常是很有意思的。如果没有缺失值，则可以将非参数方法（例如内核平滑估计）应用于每个子种群，以估计密度函数。在缺少子群体成员资格的情况下，仅使用具有可用成员资格的主题的内核平滑估计仅在完全随机缺失（MCAR）下有效。在本文中，我们通过应用随机缺失假设下的隶属度预测模型，为密度函数估计提出了一种新的核平滑方法。新估计的渐近性质得以发展，