|
" Bilinear regression analysis : "
Dietrich von Rosen.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
865780
|
| Main Entry
|
:
|
Rosen, Dietrich von
|
| Title & Author
|
:
|
Bilinear regression analysis : : an introduction /\ Dietrich von Rosen.
|
| Publication Statement
|
:
|
Cham, Switzerland :: Springer,, 2018.
|
| Series Statement
|
:
|
Lecture notes in statistics,; 220
|
| Page. NO
|
:
|
1 online resource (xiii, 468 pages) :: illustrations
|
| ISBN
|
:
|
3319787845
|
|
|
:
|
: 9783319787848
|
|
|
:
|
3319787829
|
|
|
:
|
9783319787824
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references and indexes.
|
| Contents
|
:
|
Intro; Preface; Contents; 1 Introduction; 1.1 What Is Statistics; 1.2 What Is a Statistical Model; 1.3 The General Univariate Linear Model with a Known Dispersion; 1.4 The General Multivariate Linear Model; 1.5 Bilinear Regression Models: An Introduction; Problems; Problems; Literature; References; 2 The Basic Ideas of Obtaining MLEs: A Known Dispersion; 2.1 Introduction; 2.2 Linear Models with a Focus on the Singular Gauss-Markov Model; 2.3 Multivariate Linear Models; 2.4 BRM with a Known Dispersion Matrix; 2.5 EBRMBm with a Known Dispersion Matrix; 2.6 EBRMWm with a Known Dispersion Matrix.
|
|
|
:
|
4.6 Moments of Estimators of Parameters in the EBRMB34.7 EBRMW3 and Uniqueness Conditions for MLEs; 4.8 Asymptotic Properties of Estimators of Parameters in the EBRMW3; 4.9 Moments of Estimators of Parameters in the EBRMW3; Problems; Literature; References; 5 Density Approximations; 5.1 Introduction; 5.2 Preparation; 5.3 Density Approximation for the Mean Parameter in the BRM; 5.4 Density Approximation for the Mean Parameter Estimators in the EBRMB3; 5.5 Density Approximation for the Mean Parameter Estimators in the EBRMW3; Problems; Problems; Literature; References; 6 Residuals.
|
|
|
:
|
6.1 Introduction6.2 Residuals for the BRM; 6.3 Distribution Approximations of the Residuals in the BRM; 6.4 Mean Shift Evaluations of the Residuals in the BRM; 6.5 Residual Analysis for R1 in the BRM; 6.6 Residuals for the EBRMB3; 6.7 Residuals for the EBRMW3; Problems; Problems; Literature; References; 7 Testing Hypotheses; 7.1 Introduction; 7.2 Background; 7.3 Likelihood Ratio Testing, H0:FBG=0, in the BRM; 7.4 Likelihood Ratio Testing H0:F1BG1=0 in the BRM with the Restrictions F2BG2=0, C(F1)C(F2).
|
|
|
:
|
7.5 Likelihood Ratio Testing H0:F2BG2=0 in the BRM with the Restrictions F1BG1=0, C(F1)C(F2) and C(G2)C(G1)7.6 Likelihood Ratio Testing H0:FiBGi=0, i=1,2, Against B Unrestricted in the BRM with C(F1)C(F2); 7.7 Likelihood Ratio Testing H0:FiBGi=0, i=1,2, Against B Unrestricted in the BRM with C(F1)C(F2) and C(G2)C(G1); 7.8 A ``Trace Test'' for the BRM, H0:FBG=0 Against Unrestricted B; 7.9 A ``Trace Test'' for the BRM, H0:FiBGi=0, i=1,2, C(F1)C(F2), Against Unrestricted B; 7.10 The Likelihood Ratio Test Versus the ``Trace Test''; 7.11 Testing an EBRMB3 Against a BRM.
|
|
|
:
|
ProblemsLiterature; Literature; References; 3 The Basic Ideas of Obtaining MLEs: Unknown Dispersion; 3.1 Introduction; 3.2 BRM and Its MLEs; 3.3 EBRMB3 and Its MLEs; 3.4 EBRMW3 and Its MLEs; 3.5 Reasons for Using Both the EBRMB3 and the EBRMW3; Problems; Problems; Literature; References; 4 Basic Properties of Estimators; 4.1 Introduction; 4.2 Asymptotic Properties of Estimators of Parameters in the BRM; 4.3 Moments of Estimators of Parameters in the BRM; 4.4 EBRMB3 and Uniqueness Conditions for MLEs; 4.5 Asymptotic Properties of Estimators of Parameters in the EBRMB3.
|
| Abstract
|
:
|
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.
|
| Subject
|
:
|
Regression analysis.
|
| Subject
|
:
|
Algebra.
|
| Subject
|
:
|
MATHEMATICS-- Applied.
|
| Subject
|
:
|
MATHEMATICS-- Probability Statistics-- General.
|
| Subject
|
:
|
Probability statistics.
|
| Subject
|
:
|
Regression analysis.
|
| Dewey Classification
|
:
|
519.5/36
|
| LC Classification
|
:
|
QA278.2
|
| |