{"title":"A criterion for estimating the largest linear homoscedastic zone in Gaussian data","authors":"","doi":"10.1016/j.jspi.2024.106223","DOIUrl":null,"url":null,"abstract":"<div><p>A criterion is constructed to identify the largest homoscedastic region in a Gaussian dataset. This can be reduced to a one-sided non-parametric break detection, knowing that up to a certain index the output is governed by a linear homoscedastic model, while after this index it is different (<em>e.g.</em> a different model, different variables, different volatility, ….). We show the convergence of the estimator of this index, with asymptotic concentration inequalities that can be exponential. A criterion and convergence results are derived when the linear homoscedastic zone is bounded by two breaks on both sides. Additionally, a criterion for choosing between zero, one, or two breaks is proposed. Monte Carlo experiments will also confirm its very good numerical performance.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Planning and Inference","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375824000806","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
A criterion is constructed to identify the largest homoscedastic region in a Gaussian dataset. This can be reduced to a one-sided non-parametric break detection, knowing that up to a certain index the output is governed by a linear homoscedastic model, while after this index it is different (e.g. a different model, different variables, different volatility, ….). We show the convergence of the estimator of this index, with asymptotic concentration inequalities that can be exponential. A criterion and convergence results are derived when the linear homoscedastic zone is bounded by two breaks on both sides. Additionally, a criterion for choosing between zero, one, or two breaks is proposed. Monte Carlo experiments will also confirm its very good numerical performance.
期刊介绍：
The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists.
We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.
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