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Empirical likelihood inference for missing survey data under unequal probability sampling

机译：不等概率抽样下缺失调查数据的经验似然推断

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摘要

Item nonresponse is frequently encountered in sample surveys. Hot-deck imputation is commonly used to fill in missing item values within homogeneous groups called imputation classes. We propose a fractional hot-deck imputation procedure and an associated empirical likelihood for inference on the population mean of a function of a variable of interest with missing data under probability proportional to size sampling with negligible sampling fractions. We derive the limiting distributions of the maximum empirical likelihood estimator and empirical likelihood ratio, and propose two related asymptotically valid bootstrap procedures to construct confidence intervals for the population mean. Simulation studies show that the proposed bootstrap procedures outperform the customary bootstrap procedures which are shown to be asymptotically incorrect when the number of random draws in the fractional imputation is fixed. Moreover, the proposed bootstrap procedure based on the empirical likelihood ratio is seen to perform significantly better than the method based on the limiting distribution of the maximum empirical likelihood estimator when the inclusion probabilities vary considerably or when the sample size is not large.
机译：样本调查中经常遇到项目无响应。热甲板插补通常用于填充称为插补类的同类组中的缺失项值。我们提出了分数阶热插值插补程序和相关的经验似然，以根据与样本量比例可忽略的大小抽样成比例的概率，缺少数据的目标变量的总体均值进行推断。我们推导了最大经验似然估计量和经验似然比的极限分布，并提出了两种相关的渐近有效自举程序来构建总体均值的置信区间。仿真研究表明，提出的引导程序要优于常规的引导程序，当分数插补中的随机抽取次数固定时，该引导程序在渐近性上是不正确的。此外，当包含概率变化很大或样本量不大时，基于经验似然比的自举程序被认为比基于最大经验似然估计器的极限分布的方法明显更好。

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