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E-raamat: Bilinear Regression Analysis: An Introduction

  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Statistics 220
  • Ilmumisaeg: 02-Aug-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319787848
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Bilinear Regression Analysis: An IntroductionSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Statistics 220
  • Ilmumisaeg: 02-Aug-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319787848
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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.


Arvustused

It is an interesting book, strongly recommended to researchers who have an interest in the topic of bilinear regression. (Michel H. Montoril, Mathematical Reviews, August, 2019) The present book offers a complete presentation of the statistical techniques concerning bilinear regression analysis. A special mention goes to the bibliography that accompanies each chapter. Far from being a simple list of papers containing the results recalled in the text, it is a real history of statistics, where the early ideas of bilinear regression are highlighted. (Fabio Rapallo, zbMATH 1398.62003, 2018)

1 Introduction
1(38)
1.1 What Is Statistics
1(1)
1.2 What Is a Statistical Model
2(4)
1.3 The General Univariate Linear Model with a Known Dispersion
6(5)
1.4 The General Multivariate Linear Model
11(2)
1.5 Bilinear Regression Models: An Introduction
13(26)
Problems
25(1)
Literature
26(6)
References
32(7)
2 The Basic Ideas of Obtaining MLEs: A Known Dispersion
39(32)
2.1 Introduction
39(1)
2.2 Linear Models with a Focus on the Singular Gauss-Markov Model
39(10)
2.3 Multivariate Linear Models
49(1)
2.4 BRM with a Known Dispersion Matrix
50(3)
2.5 EBRMMB with a Known Dispersion Matrix
53(9)
2.6 EBRMMW with a Known Dispersion Matrix
62(9)
Problems
65(1)
Literature
66(2)
References
68(3)
3 The Basic Ideas of Obtaining MLEs: Unknown Dispersion
71(28)
3.1 Introduction
71(1)
3.2 BRM and Its MLEs
71(8)
3.3 EBRM3B and Its MLEs
79(6)
3.4 EBRM3W and Its MLEs
85(5)
3.5 Reasons for Using Both the EBRM3B and the EBRM3W
90(9)
Problems
91(1)
Literature
92(3)
References
95(4)
4 Basic Properties of Estimators
99(78)
4.1 Introduction
99(2)
4.2 Asymptotic Properties of Estimators of Parameters in the BRM
101(3)
4.3 Moments of Estimators of Parameters in the BRM
104(15)
4.4 EBRM3B and Uniqueness Conditions for MLEs
119(4)
4.5 Asymptotic Properties of Estimators of Parameters in the EBRM3B
123(5)
4.6 Moments of Estimators of Parameters in the EBRM3B
128(29)
4.7 EBRM3W and Uniqueness Conditions for MLEs
157(2)
4.8 Asymptotic Properties of Estimators of Parameters in the EBRM3W
159(1)
4.9 Moments of Estimators of Parameters in the EBRM3W
160(17)
Problems
172(1)
Literature
173(1)
References
174(3)
5 Density Approximations
177(44)
5.1 Introduction
177(1)
5.2 Preparation
178(7)
5.3 Density Approximation for the Mean Parameter in the BRM
185(7)
5.4 Density Approximation for the Mean Parameter Estimators in the EBRM3B
192(14)
5.5 Density Approximation for the Mean Parameter Estimators in The EBRM3W
206(15)
Problems
215(1)
Literature
216(2)
References
218(3)
6 Residuals
221(60)
6.1 Introduction
221(4)
6.2 Residuals for the BRM
225(6)
6.3 Distribution Approximations of the Residuals in the BRM
231(6)
6.4 Mean Shift Evaluations of the Residuals in the BRM
237(14)
6.5 Residual Analysis for R1, in the BRM
251(5)
6.6 Residuals for the EBRM3B
256(11)
6.7 Residuals for the EBRM3W
267(14)
Problems
276(1)
Literature
277(2)
References
279(2)
7 Testing Hypotheses
281(82)
7.1 Introduction
281(1)
7.2 Background
281(5)
7.3 Likelihood Ratio Testing, H0: FBG = 0, in the BRM
286(13)
7.4 Likelihood Ratio Testing H0: F1BG1 = 0 in the BRM with the Restrictions F2BG2 = 0, C(F1) ⊂ C(F'2)
299(7)
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)
306(6)
7.6 Likelihood Ratio Testing H0: FiBGi = 0, i = 1,2, Against B Unrestricted in the BRM with C(Fi) ⊂ C(F2)
312(5)
7.7 Likelihood Ratio Testing H0: FiBGi = 0, i = 1,2, Against B Unrestricted in the BRM with C(F1) ⊂ C(F'2) and C(G2) ⊂ C(G1)
317(6)
7.8 A "Trace Test" for the BRM, H0: FBG = 0 Against Unrestricted B
323(14)
7.9 A "Trace Test" for the BRM, H0: Fi BGi = 0, i = 1,2, C(F1) ⊂ C(F2), Against Unrestricted B
337(5)
7.10 The Likelihood Ratio Test Versus the "Trace Test"
342(1)
7.11 Testing an EBRM3B Against a RBM
343(7)
7.12 Estimating and Testing in the BRM with F1BG1 = F2 ⊂ G2
350(13)
Problems
354(1)
Literature
355(3)
References
358(5)
8 Influential Observations
363(60)
8.1 Introduction
363(2)
8.2 Influence Analysis in Univariate Linear Models
365(8)
8.3 Influence Analysis in the BRM
373(20)
8.4 Influence Analysis in the EBRM3B
393(14)
8.5 Influence Analysis in the EBRM3W
407(16)
Problems
413(1)
Literature
413(4)
References
417(6)
Appendices
423(34)
Appendix A Notation
423(8)
Appendix B Useful Technical Results
431(19)
Problems
448(2)
Appendix C Test Statistics
450(7)
References
455(2)
Subject Index 457(6)
Index -- Theorems and Corollaries 463(4)
Index -- Figures and Tables 467
Dietrich von Rosen is a professor at the Department of Energy and Technology at the Swedish University of Agricultural Sciences. He graduated in mathematical statistics from Stockholm University, Sweden. His main research interest is multivariate analysis and its extensions, including repeated measurements analysis and high-dimensional analysis. He has published more than 100 papers, the majority of which are within the above areas, as well as a book on advanced multivariate statistics and matrices in collaboration with Tõnu Kollo, professor of mathematical statistics at the University of Tartu, Estonia.
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