Optimal Predictors of General Small Area Parameters Under an Informative Sample Design Using Parametric Sample Distribution Models

IF 1.6 4区数学 Q2 SOCIAL SCIENCES, MATHEMATICAL METHODS

Journal of Survey Statistics and Methodology Pub Date : 2024-03-28 DOI:10.1093/jssam/smae007

Yang Ha Cho, María Guadarrama-Sanz, Isabel Molina, A. Eideh, Emily Berg

{"title":"Optimal Predictors of General Small Area Parameters Under an Informative Sample Design Using Parametric Sample Distribution Models","authors":"Yang Ha Cho, María Guadarrama-Sanz, Isabel Molina, A. Eideh, Emily Berg","doi":"10.1093/jssam/smae007","DOIUrl":null,"url":null,"abstract":"\n Two challenges in small area estimation occur when (i) the sample selection mechanism depends on the outcome variable and (ii) the parameter of interest is a nonlinear function of the response variable in the assumed model. If, given the values of the model covariates, the sample selection mechanism depends on the model response variable, the design is said to be informative for the model. Pfeffermann and Sverchkov (2007) develop a small area estimation procedure for informative sampling, focusing on the prediction of small area means. Molina and Rao (2010) develop a small area estimation procedure for general parameters that are nonlinear functions of the model response variable. The method of Molina and Rao assumes noninformative sampling. We combine these two approaches to develop a procedure for the estimation of general parameters in small areas under informative sampling. We introduce a parametric bootstrap MSE estimator that is appropriate for an informative sample design. We evaluate the validity of the proposed procedures through extensive simulation studies and illustrate the procedures utilizing Mexico’s income data.","PeriodicalId":17146,"journal":{"name":"Journal of Survey Statistics and Methodology","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Survey Statistics and Methodology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/jssam/smae007","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"SOCIAL SCIENCES, MATHEMATICAL METHODS","Score":null,"Total":0}

引用次数: 0

Abstract

Two challenges in small area estimation occur when (i) the sample selection mechanism depends on the outcome variable and (ii) the parameter of interest is a nonlinear function of the response variable in the assumed model. If, given the values of the model covariates, the sample selection mechanism depends on the model response variable, the design is said to be informative for the model. Pfeffermann and Sverchkov (2007) develop a small area estimation procedure for informative sampling, focusing on the prediction of small area means. Molina and Rao (2010) develop a small area estimation procedure for general parameters that are nonlinear functions of the model response variable. The method of Molina and Rao assumes noninformative sampling. We combine these two approaches to develop a procedure for the estimation of general parameters in small areas under informative sampling. We introduce a parametric bootstrap MSE estimator that is appropriate for an informative sample design. We evaluate the validity of the proposed procedures through extensive simulation studies and illustrate the procedures utilizing Mexico’s income data.

查看原文本刊更多论文

使用参数样本分布模型的信息样本设计下一般小面积参数的最佳预测因子

当 (i) 样本选择机制取决于结果变量和 (ii) 相关参数是假定模型中响应变量的非线性函数时，小区域估算就会面临两个挑战。如果在给定模型协变量值的情况下，样本选择机制取决于模型响应变量，则称该设计对模型具有参考价值。Pfeffermann 和 Sverchkov（2007 年）开发了信息抽样的小面积估计程序，重点是预测小面积均值。Molina 和 Rao（2010 年）为模型响应变量的非线性函数的一般参数开发了一种小面积估计程序。Molina 和 Rao 的方法假设了非信息抽样。我们将这两种方法结合起来，开发了一种在信息抽样条件下估计小区域一般参数的程序。我们引入了适合信息抽样设计的参数自举 MSE 估计器。我们通过大量的模拟研究来评估所提出程序的有效性，并利用墨西哥的收入数据来说明这些程序。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Survey Statistics and Methodology Multiple-

CiteScore

4.30

自引率

9.50%

发文量

期刊介绍： The Journal of Survey Statistics and Methodology, sponsored by AAPOR and the American Statistical Association, began publishing in 2013. Its objective is to publish cutting edge scholarly articles on statistical and methodological issues for sample surveys, censuses, administrative record systems, and other related data. It aims to be the flagship journal for research on survey statistics and methodology. Topics of interest include survey sample design, statistical inference, nonresponse, measurement error, the effects of modes of data collection, paradata and responsive survey design, combining data from multiple sources, record linkage, disclosure limitation, and other issues in survey statistics and methodology. The journal publishes both theoretical and applied papers, provided the theory is motivated by an important applied problem and the applied papers report on research that contributes generalizable knowledge to the field. Review papers are also welcomed. Papers on a broad range of surveys are encouraged, including (but not limited to) surveys concerning business, economics, marketing research, social science, environment, epidemiology, biostatistics and official statistics. The journal has three sections. The Survey Statistics section presents papers on innovative sampling procedures, imputation, weighting, measures of uncertainty, small area inference, new methods of analysis, and other statistical issues related to surveys. The Survey Methodology section presents papers that focus on methodological research, including methodological experiments, methods of data collection and use of paradata. The Applications section contains papers involving innovative applications of methods and providing practical contributions and guidance, and/or significant new findings.