{"title":"Inference in a linear functional relationship with replications","authors":"Julio Hokama, P. Morettin, H. Bolfarine, M. Galea","doi":"10.1214/21-bjps498","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a model for data analysis with measurement errors. The main objective of this work is to develop statistical inference tools, such as parameter estimation and hypothesis tests in a linear functional relationship with replicated observations. For this purpose, we use the maximum likelihood method in the presence of incidental parameters, and the unbiased estimating equations approach. Both approaches lead to explicit expressions for the asymptotic covariance matrices of the estimators of the model parameters. A simulation study is performed to assess the empirical behavior of estimators and of a Wald statistic. The methodology is illustrated with a real data set.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-bjps498","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we consider a model for data analysis with measurement errors. The main objective of this work is to develop statistical inference tools, such as parameter estimation and hypothesis tests in a linear functional relationship with replicated observations. For this purpose, we use the maximum likelihood method in the presence of incidental parameters, and the unbiased estimating equations approach. Both approaches lead to explicit expressions for the asymptotic covariance matrices of the estimators of the model parameters. A simulation study is performed to assess the empirical behavior of estimators and of a Wald statistic. The methodology is illustrated with a real data set.
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.