Olkin and Spiegelman introduced a semiparametric estimator of the density defined as a mixture between the maximum likelihood estimator and the kernel density estimator. Due to the absence of any leave-one-out strategy and the hardness of estimating the Kullback–Leibler loss of kernel density estimate, their approach produces unsatisfactory results. This article investigates an alternative approach in which only the kernel density estimate is modified. From a theoretical perspective, the estimated mixture parameter is shown to converge in probability to one if the parametric model is true and to zero otherwise. From a practical perspective, the utility of the approach is illustrated on real and simulated data sets.

中文翻译：

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参数与非参数：适应度系数

Olkin 和 Spiegelman 引入了密度的半参数估计，定义为最大似然估计和核密度估计之间的混合。由于缺乏任何留一法策略以及估计核密度估计的 Kullback-Leibler 损失的难度，他们的方法产生了不令人满意的结果。本文研究了一种仅修改核密度估计的替代方法。从理论的角度来看，如果参数模型为真，则估计的混合参数显示为收敛到 1，否则收敛到 0。从实际的角度来看，该方法的实用性在真实和模拟数据集上进行了说明。