{"title":"Matrix-variate generalized linear model with measurement error","authors":"Tianqi Sun, Weiyu Li, Lu Lin","doi":"10.1007/s00362-024-01540-6","DOIUrl":null,"url":null,"abstract":"<p>Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because matrix-form data can be regarded as a specific tensor (2-dimension). But there are few works focusing on matrix-form data with measurement error (ME), since tensor in conjunction with ME is relatively complex in structure. In this paper we introduce a mvGLM to primarily explore the influence of ME in the model with matrix-form data. We calculate the asymptotic bias based on error-prone mvGLM, and then develop bias-correction methods to tackle the affect of ME. Statistical properties for all methods are established, and the practical performance of all methods is further evaluated in analysis on synthetic and real data sets.</p>","PeriodicalId":51166,"journal":{"name":"Statistical Papers","volume":"55 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-04-06","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/s00362-024-01540-6","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
Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because matrix-form data can be regarded as a specific tensor (2-dimension). But there are few works focusing on matrix-form data with measurement error (ME), since tensor in conjunction with ME is relatively complex in structure. In this paper we introduce a mvGLM to primarily explore the influence of ME in the model with matrix-form data. We calculate the asymptotic bias based on error-prone mvGLM, and then develop bias-correction methods to tackle the affect of ME. Statistical properties for all methods are established, and the practical performance of all methods is further evaluated in analysis on synthetic and real data sets.
在张量广义线性模型的框架下，矩阵变量广义线性模型（mvGLM）已经得到了成功的研究，因为矩阵形式的数据可以被视为一个特定的张量（二维）。但是，由于带有测量误差（ME）的张量结构相对复杂，因此关注带有测量误差（ME）的矩阵形式数据的研究很少。在本文中，我们引入了 mvGLM，主要探讨 ME 在矩阵形式数据模型中的影响。我们基于易出错的 mvGLM 计算渐近偏差，然后开发偏差修正方法来解决 ME 的影响。我们建立了所有方法的统计特性，并通过对合成数据集和真实数据集的分析进一步评估了所有方法的实际性能。
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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