在分层简单随机抽样下用于估计和预测的一种统一方法(英文)

A Unified Approach to Estimation and Prediction Under Stratified Simple Random Sampling

考虑由服从随机置换概率分布的随机变量扩张集组成的概率模型,利用Stanek文中的方法,给出了单元参数性组合的最优估计和随机效应的最优预测,总体均值的最小方差无偏估计是样本均值;而当单元被取入样本中时,单元参数的最小方差无偏估计是Horvitz-Thompson估计量,否则为零.

We consider a probability model which consists of an expanded set of random variables following a random permutation probability distribution that keeps track of both the unit＇s labels and positions in the permutation. Following the approach of Stanek, we develop optimum estimators of the linear combinations of the unit parameters and optimum predictors of the random effects is developed. The unbiased minimum variance estimator of the population mean is the sample mean and of a unit parameter is the Hovitz-Thompson estimator if the unit is included in the sample, and zero otherwise.