Statistical inference with empty strata in judgment post stratified samples
A judgment post stratified (JPS) sample can be briefly indicated as follows. A JPS sample consists of a simple random sample (SRS) \((X_1,\dots,X_n)\) and a rank vector \(R=(R_1,\dots,R_n)\) associated with \(X_i\), \(i=1,2,\dots,n\) in SRS. The author first constructs a conditional JPS sample with a reduced size \(K\) by conditioning on the ranks of the measured observations of the original JPS sample of set size \(H\geq K\). Then it is shown that the estimators based on the conditional JPS sample for the population mean, median and distribution function, are consistent and have limiting normal distribution. It is further shown that the proposed estimators, unlike the ratio and regression estimators, only require a certain monotonic relationship between response and auxiliary variable. For moderate sample sizes the author uses a bootstrap method to make statistical inference. A small-scale simulation is included to show that the proposed estimators based on reduced set JPS sample perform better than the corresponding estimators based on a regular JPS sample.
scientific article; zbMATH DE number 6807782
scientific article