QUANTILE PROCESSES AND THEIR APPLICATIONS IN FINITE POPULATIONS

• 成果类型: Article
• 署名作者: Dey, Anurag; Chaudhuri, Probal
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Kolkata
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2432
• 发表日期: 2024
• 页码: 2194-2216
• 关键词: Asymptotic Normality; variance-estimation; sampling designs; LIMIT-THEOREMS; estimators; horvitz

摘要

The weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles, is shown under various well-known sampling designs based on a superpopulation model. The results related to the weak convergence of these quantile processes are applied to find asymptotic distributions of the smooth L-estimators and the estimators of smooth functions of finite population quantiles. Based on these asymptotic distributions, confidence intervals are constructed for several finite population parameters like the median, the alpha-trimmed means, the interquartile range and the quantile based measure of skewness. Comparisons of various estimators are carried out based on their asymptotic distributions. We show that the use of the auxiliary information in the construction of the estimators sometimes has an adverse effect on the performances of the smooth Lestimators and the estimators of smooth functions of finite population quantiles under several sampling designs. Further, the performance of each of the above-mentioned estimators sometimes becomes worse under sampling designs, which use the auxiliary information, than their performances under simple random sampling without replacement (SRSWOR).