ABSTRACT We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The asymptotic normality is proved under both design and combined spaces. Two data driven estimators are proposed based on the proposed oracle estimator. We show the efficiency of the proposed estimators in simulation studies. A real survey data example is provided for an illustration.

中文翻译：

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复杂调查的正交系列密度估计

摘要 我们提出了一种用于复杂调查的正交序列密度估计器，其中样本既不是独立的也不是同分布的。所提出的估计量被证明是设计无偏的和渐近设计一致的。在设计空间和组合空间下都证明了渐近正态性。在提出的预言机估计器的基础上提出了两个数据驱动的估计器。我们在模拟研究中展示了提议的估计器的效率。提供了一个真实的调查数据示例以供说明。