{"title":"平方根变换下计数数据小面积估计的单位级模型","authors":"Kelly C. M. Gonçalves, M. Ghosh","doi":"10.1214/21-bjps513","DOIUrl":null,"url":null,"abstract":"Abstract. In recent years, the demand for small area statistics has greatly increased worldwide. Small area models are formulated with random area-specific effects assumed to account for the between-area variation that is not explained by auxiliary variables. The unit level models relate the unit values of a study variable to unit-specific covariates. The main aim of this paper is to consider small area estimation under unit level models based on count data. In particular, instead of modelling the variables assuming the Poisson distribution, which is a usual choice, we consider the square root transformation of the original data. One practical advantage is that the proposed transformation achieves approximate homoscedasticity of the error variances, reducing one layer of estimation problem. Inference for the model is carried out under the hierarchical Bayes approach. The square root transformation is evaluated under a simulation study and two design-based studies with real datasets.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Unit level model for small area estimation with count data under square root transformation\",\"authors\":\"Kelly C. M. Gonçalves, M. Ghosh\",\"doi\":\"10.1214/21-bjps513\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. In recent years, the demand for small area statistics has greatly increased worldwide. Small area models are formulated with random area-specific effects assumed to account for the between-area variation that is not explained by auxiliary variables. The unit level models relate the unit values of a study variable to unit-specific covariates. The main aim of this paper is to consider small area estimation under unit level models based on count data. In particular, instead of modelling the variables assuming the Poisson distribution, which is a usual choice, we consider the square root transformation of the original data. One practical advantage is that the proposed transformation achieves approximate homoscedasticity of the error variances, reducing one layer of estimation problem. Inference for the model is carried out under the hierarchical Bayes approach. The square root transformation is evaluated under a simulation study and two design-based studies with real datasets.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/21-bjps513\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-bjps513","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Unit level model for small area estimation with count data under square root transformation
Abstract. In recent years, the demand for small area statistics has greatly increased worldwide. Small area models are formulated with random area-specific effects assumed to account for the between-area variation that is not explained by auxiliary variables. The unit level models relate the unit values of a study variable to unit-specific covariates. The main aim of this paper is to consider small area estimation under unit level models based on count data. In particular, instead of modelling the variables assuming the Poisson distribution, which is a usual choice, we consider the square root transformation of the original data. One practical advantage is that the proposed transformation achieves approximate homoscedasticity of the error variances, reducing one layer of estimation problem. Inference for the model is carried out under the hierarchical Bayes approach. The square root transformation is evaluated under a simulation study and two design-based studies with real datasets.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.