{"title":"Maximum spacing estimation for multivariate observations under a general class of information-type measures","authors":"Kristi Kuljus , Han Bao , Bo Ranneby","doi":"10.1016/j.jmva.2025.105433","DOIUrl":null,"url":null,"abstract":"<div><div>This article considers the maximum spacing (MSP) method for multivariate observations, nearest neighbour balls are used as a multidimensional analogue to univariate spacings. Compared to the previous studies, a broader class of MSP estimators corresponding to different information-type measures is studied. The studied class of estimators includes also the estimator corresponding to the Kullback–Leibler information measure obtained with the logarithmic function. Consistency of the MSP estimators is proved when the assigned model class is correct, that is the true density belongs to the assigned class. The behaviour of the MSP estimator under different divergence measures is studied and the advantage of using MSP estimators corresponding to different information measures in the context of model validation is illustrated in simulation examples.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105433"},"PeriodicalIF":1.4000,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X25000284","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
This article considers the maximum spacing (MSP) method for multivariate observations, nearest neighbour balls are used as a multidimensional analogue to univariate spacings. Compared to the previous studies, a broader class of MSP estimators corresponding to different information-type measures is studied. The studied class of estimators includes also the estimator corresponding to the Kullback–Leibler information measure obtained with the logarithmic function. Consistency of the MSP estimators is proved when the assigned model class is correct, that is the true density belongs to the assigned class. The behaviour of the MSP estimator under different divergence measures is studied and the advantage of using MSP estimators corresponding to different information measures in the context of model validation is illustrated in simulation examples.
期刊介绍：
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.
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