{"title":"Semiparametric density estimation with localized Bregman divergence","authors":"Daisuke Matsuno , Kanta Naito","doi":"10.1016/j.jmva.2025.105419","DOIUrl":null,"url":null,"abstract":"<div><div>This paper examines semiparametric density estimation by combining a parametric crude guess and its nonparametric adjustment. The nonparametric adjustment is implemented via minimization of the localized Bregman divergence, which yields a broad class of semiparametric density estimators. Asymptotic theories of the density estimators in this general class are developed. Specific concrete forms of density estimators under a certain divergence and parametric guess are calculated. Simulations for several target densities and application to a real data set reveal that the proposed density estimators offer competitive or, in some cases, better performance compared to fully nonparametric kernel density estimator.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105419"},"PeriodicalIF":1.4000,"publicationDate":"2025-01-30","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/S0047259X25000144","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 paper examines semiparametric density estimation by combining a parametric crude guess and its nonparametric adjustment. The nonparametric adjustment is implemented via minimization of the localized Bregman divergence, which yields a broad class of semiparametric density estimators. Asymptotic theories of the density estimators in this general class are developed. Specific concrete forms of density estimators under a certain divergence and parametric guess are calculated. Simulations for several target densities and application to a real data set reveal that the proposed density estimators offer competitive or, in some cases, better performance compared to fully nonparametric kernel density estimator.
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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