{"title":"Implicit profiling estimation for semiparametric models with bundled parameters","authors":"","doi":"10.1007/s00362-023-01519-9","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton’s method becomes quite slow and unstable with an intensive calculation of the large Hessian matrix and its inverse. Iterative methods separately updating parameters for the finite dimensional component and the infinite dimensional component have been developed to speed up single iterations, but they often take more steps until convergence or even sometimes sacrifice estimation precision due to sub-optimal update direction. We propose a computationally efficient implicit profiling algorithm that achieves simultaneously the fast iteration step in iterative methods and the optimal update direction in Newton’s method by profiling out the infinite dimensional component as the function of the finite-dimensional component. We devise a first-order approximation when the profiling function has no explicit analytical form. We show that our implicit profiling method always solves any local quadratic programming problem in two steps. In two numerical experiments under semiparametric transformation models and GARCH-M models, as well as a real application using NTP data, we demonstrated the computational efficiency and statistical precision of our implicit profiling method. Finally, we implement the proposed implicit profiling method in the R package <em>SemiEstimate</em></p>","PeriodicalId":51166,"journal":{"name":"Statistical Papers","volume":"13 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Papers","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00362-023-01519-9","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
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton’s method becomes quite slow and unstable with an intensive calculation of the large Hessian matrix and its inverse. Iterative methods separately updating parameters for the finite dimensional component and the infinite dimensional component have been developed to speed up single iterations, but they often take more steps until convergence or even sometimes sacrifice estimation precision due to sub-optimal update direction. We propose a computationally efficient implicit profiling algorithm that achieves simultaneously the fast iteration step in iterative methods and the optimal update direction in Newton’s method by profiling out the infinite dimensional component as the function of the finite-dimensional component. We devise a first-order approximation when the profiling function has no explicit analytical form. We show that our implicit profiling method always solves any local quadratic programming problem in two steps. In two numerical experiments under semiparametric transformation models and GARCH-M models, as well as a real application using NTP data, we demonstrated the computational efficiency and statistical precision of our implicit profiling method. Finally, we implement the proposed implicit profiling method in the R package SemiEstimate
期刊介绍：
The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.
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