Bilinear regression analysis : an introduction /: an introduction. (2018)

• Record Type: Book
• Further Information: Note: Dietrich von Rosen.
• Authors: Rosen, Dietrich von
• 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. 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. 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (xiii, 468 pages), illustrations
• Subjects: 519.5/36; Statistics; Regression analysis; Mathematical statistics; Matrix theory; MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Regression analysis; Mathematics -- Algebra -- Linear; Medical -- Biostatistics; Algebra; Probability & statistics; Electronic books
• Languages: English
• ISBNs: 9783319787848; 3319787845
• Related ISBNs: 9783319787824; 3319787829
• Notes: Note: Includes bibliographical references and indexes.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 9, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.