Michael T. Gorczyca, Tavish M. McDonald, Justice D. Sefas
{"title":"A note on trigonometric regression in the presence of Berkson‐type measurement error","authors":"Michael T. Gorczyca, Tavish M. McDonald, Justice D. Sefas","doi":"10.1111/stan.12344","DOIUrl":null,"url":null,"abstract":"In this note, we study how parameter vector estimation for a trigonometric regression model and the expected squared residual error computed from an estimated model are affected by Berkson‐type measurement error. Closed‐form expressions for the parameter vector and the expected squared residual error are obtained by assuming that the observed covariate data are sampled from an equispaced design and that measurement error is generated from a symmetric probability distribution with a mean of zero. Notably, these results indicate that estimates of the amplitude parameters for a trigonometric regression model suffer from attenuation bias when covariate data are mis‐measured, and that estimates of the phase‐shift parameters are unbiased.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"80 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistica Neerlandica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1111/stan.12344","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we study how parameter vector estimation for a trigonometric regression model and the expected squared residual error computed from an estimated model are affected by Berkson‐type measurement error. Closed‐form expressions for the parameter vector and the expected squared residual error are obtained by assuming that the observed covariate data are sampled from an equispaced design and that measurement error is generated from a symmetric probability distribution with a mean of zero. Notably, these results indicate that estimates of the amplitude parameters for a trigonometric regression model suffer from attenuation bias when covariate data are mis‐measured, and that estimates of the phase‐shift parameters are unbiased.
期刊介绍:
Statistica Neerlandica has been the journal of the Netherlands Society for Statistics and Operations Research since 1946. It covers all areas of statistics, from theoretical to applied, with a special emphasis on mathematical statistics, statistics for the behavioural sciences and biostatistics. This wide scope is reflected by the expertise of the journal’s editors representing these areas. The diverse editorial board is committed to a fast and fair reviewing process, and will judge submissions on quality, correctness, relevance and originality. Statistica Neerlandica encourages transparency and reproducibility, and offers online resources to make data, code, simulation results and other additional materials publicly available.