Multivariate reduced-rank regression : theory, methods and applications / / Gregory C. Reinsel, Rajabather Palani Velu, Kun Chen

• Record Nr.: UNISA996499866803316
• Autore: Reinsel Gregory C.
• Pubbl/distr/stampa: New York, New York : , : Springer, , 2023
• ISBN: 1-0716-2793-7
• Edizione: [Second edition.]
• Descrizione fisica: 1 online resource (420 pages) : illustrations
• Collana: Lecture notes in statistics ; ; Volume 225
• Classificazione: TKK
• Disciplina: 519.535
• Soggetti: Multivariate analysis; Regression analysis; Anàlisi multivariable; Anàlisi de regressió; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- About the Authors -- 1 Multivariate Linear Regression -- 1.1 Introduction -- 1.2 Multivariate Linear Regression Model and Least Squares Estimator -- 1.3 Further Inference Properties in the Multivariate Regression Model -- 1.4 Prediction in the Multivariate Linear Regression Model -- 1.5 Numerical Examples -- 1.5.1 Biochemical Data -- 1.5.2 Sales Performance Data -- 2 Reduced-Rank Regression Model -- 2.1 The Basic Reduced-Rank Model and Background -- 2.2 Some Examples of Application of the Reduced-Rank Model -- 2.3 Estimation of Parameters in the Reduced-Rank Model -- 2.4 Relation to Principal Components and Canonical Correlation Analysis -- 2.4.1 Principal Components Analysis -- 2.4.2 Application to Functional and Structural Relationships Models -- 2.4.3 Canonical Correlation Analysis -- 2.5 Asymptotic Distribution of Estimators in Reduced-Rank Model -- 2.6 Identification of Rank of the Regression Coefficient Matrix -- 2.7 Reduced-Rank Inverse Regression for Estimating Structural Dimension -- 2.8 Numerical Examples -- 2.9 Alternate Procedures for Analysis of Multivariate Regression Models -- 3 Reduced-Rank Regression Models with Two Sets of Regressors -- 3.1 ; Reduced-Rank Model of Anderson -- 3.2 Application to One-Way ANOVA and Linear Discriminant Analysis -- 3.3 Numerical Example Using Chemometrics Data -- 3.4 Both Regression Matrices of Lower Ranks: Model and Its Applications -- 3.5 Estimation and Inference for the Model -- 3.5.1 Efficient Estimator -- 3.5.2 An Alternative Estimator -- 3.5.3 Asymptotic Inference -- 3.6 Identification of Ranks of Coefficient Matrices -- 3.7 An Example on Ozone Data -- 3.8 Conclusion -- 4 Reduced-Rank Regression Model With Autoregressive Errors -- 4.1 Introduction and the Model.; 4.2 Example on the U.K. Economy: Basic Data and Their Descriptions -- 4.3 Maximum Likelihood Estimators for the Model -- 4.4 Computational Algorithms for Efficient Estimators -- 4.5 Alternative Estimators and Their Properties -- 4.5.1 A Comparison Between Efficient and Other Estimators -- 4.6 Identification of Rank of the Regression Coefficient Matrix -- 4.7 Inference for the Numerical Example -- 4.8 An Alternate Estimator with Kronecker Approximation -- 4.8.1 Computational Results -- 5 Multiple Time Series Modeling With Reduced Ranks -- 5.1 Introduction and Time Series Models -- 5.2 Reduced-Rank Autoregressive Models -- 5.2.1 Estimation and Inference -- 5.2.2 Relationship to Canonical Analysis of Box and Tiao -- 5.3 An Extended Reduced-Rank Autoregressive Model -- 5.4 Nested Reduced-Rank Autoregressive Models -- 5.4.1 Specification of Ranks -- 5.4.2 A Canonical Form -- 5.4.3 Maximum Likelihood Estimation -- 5.5 Numerical Example: U.S. Hog Data -- 5.6 Relationship Between Nonstationarity and Canonical Correlations -- 5.7 Cointegration for Nonstationary Series-Reduced Rank in Long Term -- 5.7.1 LS and ML Estimation and Inference -- 5.7.2 Likelihood Ratio Test for the Number of Cointegrating Relations -- 5.8 Unit Root and Cointegration Aspects for the U.S. Hog Data Example -- 6 The Growth Curve Model and Reduced-Rank Regression Methods -- 6.1 Introduction and the Growth Curve Model -- 6.2 Estimation of Parameters in the Growth Curve Model -- 6.3 Likelihood Ratio Testing of Linear Hypotheses in Growth Curve Model -- 6.4 An Extended Model for Growth Curve Data -- 6.5 Modification of Basic Growth Curve Model to Reduced-Rank Model -- 6.6 Reduced-Rank Growth Curve Models -- 6.6.1 Extensions of the Reduced-Rank Growth Curve Model -- 6.7 Application to One-way ANOVA and Linear Discriminant Analysis -- 6.8 A Numerical Example -- 6.9 Some Recent Developments.; 7 Seemingly Unrelated Regressions Models With Reduced Ranks -- 7.1 Introduction and the Seemingly Unrelated Regressions Model -- 7.2 Relation of Growth Curve Model to the Seemingly Unrelated Regressions Model -- 7.3 Reduced-Rank Coefficient in Seemingly Unrelated Regressions Model -- 7.4 Maximum Likelihood Estimators for Reduced-Rank Model -- 7.5 An Alternate Estimator and Its Properties -- 7.6 Identification of Rank of the Regression Coefficient Matrix -- 7.7 A Numerical Illustration with Scanner Data -- 7.8 Some Recent Developments -- 8 Applications of Reduced-Rank Regression in Financial Economics -- 8.1 Introduction to Asset Pricing Models -- 8.2 Estimation and Testing in the Asset Pricing Model -- 8.3 Additional Applications of Reduced-Rank Regression in Finance -- 8.4 Empirical Studies and Results on Asset Pricing Models -- 8.5 Related Topics -- 8.6 An Application -- 8.7 Cointegration and Pairs Trading -- 9 Partially Reduced-Rank Regression with Grouped Responses -- 9.1 Introduction: Partially Reduced-Rank Regression Model -- 9.2 Estimation of Parameters -- 9.3 Test for Rank and Inference Results -- 9.4 Procedures for Identification of Subset Reduced-Rank Structure -- 9.5 Illustrative Examples -- 9.6 Discussion and Extensions -- 10 High-Dimensional Reduced-Rank Regression -- 10.1 Introduction -- 10.2 ; Overview of High-Dimensional Regularized Regression -- 10.3 Framework of Singular Value Regularization -- 10.4 Reduced-Rank Regression via Adaptive Nuclear-Norm Penalization -- 10.4.1 Adaptive Nuclear Norm -- 10.4.2 Adaptive Nuclear-Norm Penalized Regression -- 10.4.3 Theoretical Analysis -- 10.4.3.1 Setup and Assumptions -- 10.4.3.2 Rank Consistency and Prediction Error Bound -- 10.5 Integrative Reduced-Rank Regression: Bridging Sparse and Low-Rank Models -- 10.5.1 Composite Nuclear-Norm Penalization -- 10.5.2 Theoretical Analysis.; 10.6 Applications -- 10.6.1 Breast Cancer Data -- 10.6.2 Longitudinal Studies of Aging -- 11 Unbiased Risk Estimation in Reduced-Rank Regression -- 11.1 Introduction -- 11.2 Degrees of Freedom -- 11.3 Degrees of Freedom of Reduced-Rank Estimation -- 11.4 Comparing Empirical and Exact Estimators -- 11.4.1 Simulation Setup -- 11.4.2 Comparing Estimators of the Degrees of Freedom -- 11.4.3 Performance on Estimating the Prediction Error -- 11.4.4 Performance on Model Selection -- 11.5 Applications -- 11.5.1 Norwegian Paper Quality Data -- 11.5.2 Arabidopsis Thaliana Data -- 12 Generalized Reduced-Rank Regression -- 12.1 Introduction -- 12.2 Robust Reduced-Rank Regression -- 12.2.1 Non-Robustness of Reduced-Rank Regression -- 12.2.2 Robustification with Sparse Mean Shift -- 12.2.3 Theoretical Analysis -- 12.3 Reduced-Rank Estimation with Incomplete Data -- 12.3.1 Noiseless Matrix Completion -- 12.3.2 Stable Matrix Completion -- 12.3.3 Computation -- 12.4 Generalized Reduced-Rank Regression with Mixed Outcomes -- 12.5 Applications -- 12.5.1 Arabidopsis Thaliana data -- 12.5.2 Longitudinal Studies of Aging -- 13 Sparse Reduced-Rank Regression -- 13.1 Introduction -- 13.2 Sparse Reduced-Rank Regression -- 13.2.1 Sparse Reduced-Rank Regression for Predictor Selection -- 13.2.2 Computation -- 13.2.3 Theoretical Analysis -- 13.3 Co-sparse Factor Regression -- 13.3.1 Model Formulation and Deflation Procedures -- 13.3.2 Co-sparse Unit-Rank Estimation -- 13.3.3 Theoretical Analysis -- 13.4 Applications -- 13.4.1 Yeast eQTL Mapping Analysis -- 13.4.2 Forecasting Macroeconomic and Financial Indices -- Appendix -- References -- Subject Index -- Reference Index.