It has been shown in the literature that judgment post stratification (JPS) sampling design often leads to more efficient statistical inference than what is possible to obtain in simple random sampling (SRS) design of comparable size. Since the JPS is a cost-efficient sampling design, a large enough sample size may not be available to use normal theory of the estimators. In this paper, we describe two bootstrap methods for JPS sampling scheme, one of which has been already used in the literature without studying its consistency and the other is new. We also show that both bootstrap approaches are consistent. We then investigate the use of the bootstrap methods for constructing confidence intervals for the population mean and compare them with the confidence interval of the population mean obtained via normal approximation (NA) method using Monte Carlo simulation. It is found that for the asymmetric distributions, one of the bootstrap methods we describe in the paper often leads to a closer coverage probability (CP) to the nominal level than NA method. Finally, a real dataset is analysed for illustration.

中文翻译：

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用于判断后分层的 Bootstrap 方法

文献中已经表明，与在可比规模的简单随机抽样 (SRS) 设计中可能获得的结果相比，判断后分层 (JPS) 抽样设计通常会导致更有效的统计推断。由于 JPS 是一种具有成本效益的抽样设计，因此可能无法使用足够大的样本量来使用估计量的正常理论。在本文中，我们描述了 JPS 采样方案的两种 bootstrap 方法，其中一种已经在文献中使用而没有研究其一致性，另一种是新的。我们还表明两种引导方法是一致的。然后，我们研究使用 bootstrap 方法构建总体均值的置信区间，并将它们与使用蒙特卡罗模拟通过正态近似 (NA) 方法获得的总体均值的置信区间进行比较。发现对于非对称分布，我们在论文中描述的其中一种 bootstrap 方法通常会导致比 NA 方法更接近标称水平的覆盖概率 (CP)。最后，分析了一个真实的数据集以供说明。