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Titlebook: Bilinear Regression Analysis; An Introduction Dietrich von Rosen Book 2018 Springer International Publishing AG, part of Springer Nature 20

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发表于 2025-3-21 16:59:16 | 显示全部楼层 |阅读模式
期刊全称Bilinear Regression Analysis
期刊简称An Introduction
影响因子2023Dietrich von Rosen
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发行地址Presents results for bilinear regression models and their connection to classical statistical multivariate analysis.Sheds new light on the notion of linear and bilinear multivariate models.Includes bo
学科分类Lecture Notes in Statistics
图书封面Titlebook: Bilinear Regression Analysis; An Introduction Dietrich von Rosen Book 2018 Springer International Publishing AG, part of Springer Nature 20
影响因子This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph.D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis..
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发表于 2025-3-21 23:41:45 | 显示全部楼层
The Basic Ideas of Obtaining MLEs: Unknown Dispersion,sitions of the tensor space where within-individuals spaces also have an inner product which has to be estimated. All obtained estimators have explicit forms. A short literature review of bilinear regression models is given.
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Basic Properties of Estimators,rived for all estimators as well as the covariance among the estimators from the same model. Calculations use knowledge about the matrix normal, Wishart and inverted Wishart distributions. It is shown that the estimators are asymptotically equivalent to normally distributed random variables.
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Density Approximations,on model the approximating density also appears to be a density. It can be shown that under some conditions the density represents a mixture of a normal distribution and a matrix Kotz-distribution. Similar results are shown to be available for the extended bilinear regression models.
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