Innovations in Multivariate Statistical Modeling: Navigating Theoretical and Multidisciplinary Domains

Description

Multivariate statistical analysis has undergone a rich and varied evolution during the latter half of the 20th century. Academics and practitioners have produced much literature with diverse interests and with varying multidisciplinary knowledge on different topics within the multivariate domain. Due to multivariate algebra being of sustained interest and being a continuously developing field, its appeal breaches laterally across multiple disciplines to act as a catalyst for contemporary advances, with its core inferential genesis remaining in that of statistics. It is exactly this varied evolution caused by an influx in data production, diffusion, and understanding in scientific fields that has blurred many lines between disciplines. The cross-pollination between statistics and biology, engineering, medical science, computer science, and even art, has accelerated the vast amount of questions that statistical methodology has to answer and report on. These questions are often multivariate in nature, hoping to elucidate uncertainty on more than one aspect at the same time, and it is here where statistical thinking merges mathematical design with real life interpretation for understanding this uncertainty. Statistical advances benefit from these algebraic inventions and expansions in the multivariate paradigm. This contributed volume aims to usher novel research emanating from a multivariate statistical foundation into the spotlight, with particular significance in multidisciplinary settings. The overarching spirit of this volume is to highlight current trends, stimulate a focus on, and connect multidisciplinary dots from and within multivariate statistical analysis. Guided by these thoughts, a collection of research at the forefront of multivariate statistical thinking is presented here which has been authored by globally recognized subject matter experts. Preface Contents About the Editors Trends in Multi- and Matrix-Variate Analysis Association-Based Optimal Subpopulation Selection for Multivariate Data 1 Introduction 2 The Proposed Method Averaged Absolute Association (AAA) Criterion Efficient Algorithms 3 Simulation Study Evaluation of Selected Subpopulation Comparisons of the Algorithms Comparison with the Tau-Path Method 4 Case Study 5 Discussion References Likelihood-Based Inference for Linear Mixed-Effects Models with Censored Response Using Skew-Normal Distribution 1 Introduction 2 The Multivariate Skew-Normal Distribution 3 The Skew-Normal Linear Mixed-Effects Model with Censored Responses The Statistical Model The Likelihood Function The ECM Algorithm Approximate Standard Errors Estimation of the Random Effects Prediction of Future Observations 4 Illustrative Example—UTI Data 5 Conclusions References Robust Estimation of Multiple Change Points in Multivariate Processes 1 Introduction 2 Methodology Matrix Normal Distribution Change Point Estimation 3 Experiments 4 Applications Illustration on Crime Rates in US Cities Effect of Colorado Amendment 64 5 Discussion References Some Computational Aspects of a Noncentral Dirichlet Family 1 Introduction 2 Foundations of the Dirichlet 3 Methods and Approach Log-Likelihood Method for Investigating lamda 3λ3 Initial Parameters for MLE Search 4 Data Fitting Simulation Study 1 Simulation Study 2 Dataset 1—Household Expenditure Data Dataset 2—Pekin Duckling Data 5 Final Thoughts and Future Directions References Modeling Handwritten Digits Dataset Using the Matrix Variate t Distribution 1 Introduction 2 Matrix Variate t Distribution 3 Parameter Estimation Maximum Likelihood Estimation Estimation via EM Algorithm 4 Simulation Study and Real Data Example Simulation Study Real Data Example 5 Conclusions References On the Identification of Extreme Elements in a Residual for the GMANOVA-MANOVA Model 1 Introduction 2 Background Residuals in the GMANOVA-MANOVA Model The GMANOVA-MANOVA Model and the Parametric Bootstrap Technique 3 Data Analysis 4 Concluding Remarks References Matrix-variate Smooth Transition Models for Temporal Networks 1 Introduction 2 A Smooth Transition Matrix Model Transition Mechanisms Nonlinear Network Models Extensions 3 Bayesian Inference Prior Specification Posterior Approximation 4 Empirical Analysis Volatility Networks Oil Production Networks 5 Conclusion References A Flexible Matrix-Valued Response Regression for Skewed Data 1 Introduction 2 Background Matrix-variate Normal Distribution Unimodal–bimodal Normal (UBN) Distribution Skewed Matrix-Variate UBN (MatUBN) Distribution 3 Proposed Regression Model Model Formulation Extending the Model Using Envelope Formulation 4 Simulation Study 5 Applications 6 Concluding References Multivariate Functional Singular Spectrum Analysis: A Nonparametric Approach for Analyzing Multivariate Functional Time Series 1 Background General Scheme of Univariate Singular Spectrum Analysis General Scheme of Functional Singular Spectrum Analysis General Scheme of Multivariate Singular Spectrum Analysis 2 General Scheme of Multivariate Functional Singular Spectrum Analysis Preliminaries and Notations Multivariate Functional Singular Spectrum Analysis Algorithm Computer Implementation Strategy 3 Generalizing Multivariate Singular Spectrum Analysis to Multivariate Functional Singular Spectrum Analysis From Horizontal Multivariate Singular Spectrum Analysis to Horizontal Multivariate Functional Singular Spectrum Analysis From Vertical Multivariate Singular Spectrum Analysis to Vertical Multivariate Functional Singular Spectrum Analysis 4 Numerical Studies Simulation Study Application to NDVI Images and Intraday Temperature Data Application to Remote Sensing Density Curves 5 Discussion References Compositional Data Analysis—Linear Algebra, Visualization and Interpretation 1 Introduction 2 Basic Algebraic Definitions and Results Logratio Transformations and Associated Pattern Matrices Inverting Logratio Transformations Log-Contrasts 3 Logratio Visualization 4 Summary and Discussion References Multivariate Count Data Regression Models and Their Applications 1 Introduction 2 Review of T-R{W} Family of Distributions Sub-Families of Discrete T-R{W} Distributions The Family of Generalized Geometric Distributions 3 Bivariate and Multivariate T-geometric{W} Families Sarmanov Family of Bivariate and Multivariate Distributions Bivariate and Multivariate T-geometric{W} Families Multivariate T-geometric{W} Regression Model 4 Inference on Bivariate and Multivariate T-geometric{W} Regression Models Test for Independence Test for Dispersion Test to Compare Nested and Non-nested Models Goodness-Of-Fit Statistics 5 Application Sex Partners Data Inmates Profiling Data 6 Summary and Conclusions 7 Appendix References A Generalized Multivariate Gamma Distribution 1 Introduction 2 The Multivariate Gamma Distribution 3 Marginal Distributions 4 Factorizations 5 Joint Moments 6 Moment Generating Function 7 Entropies 8 Estimation 9 Simulation 10 Conclusion References Aspects of High-Dimensional Methodology and Bayesian Learning A Comparison of Different Clustering Approaches for High-Dimensional Presence-Absence Data 1 Introduction 2 Data and Preprocessing 3 Clustering Methods Latent Class Analysis Methods Operating on Distances Methods Operating on Euclidean Data 4 The Simulation Data Generation Scenarios 5 Results General Results More Detailed Insight 6 Conclusions References High-Dimensional Feature Selection for Logistic Regression Using Blended Penalty Functions 1 Introduction 2 Penalised GLM with the MEnet Penalty Modified Elastic-Net Penalty Penalised Likelihood Function Reforming of the MEnet Penalty Term Parameter Estimation 3 Simulation Study 4 Colon Cancer Classification 5 Conclusion and Future Work References A Generalized Quadratic Garrote Approach Towards Ridge Regression Analysis 1 Introduction 2 Quadratic Garrote Variance and Bias 3 Simulation Study Sparse Setting Nearly-Sparse Setting High Dimensional Setting 4 Example: The Boston Housing Dataset 5 Discussion References High-Dimensional Nonlinear Optimization Problem in Semiparametric Regression Model 1 Introduction 2 Differencing Approach to Approximate the Model How Does the Approximation Work? 3 Ridge Estimation of Sparse Semiparametric Regression Model 4 Least Absolute Shrinkage and Selection Operator Approach 5 A Mathematical Heuristic Algorithm for Estimation of High-Dimensional SRM 6 Numerical studies Application to Riboflavin Production Data Set Some Simulation Studies 7 Summary and Conclusions References Frontiers in Robust Analysis and Mixture Modelling Parsimonious Finite Mixtures of Matrix-Variate Regressions 1 Introduction 2 Methodology Parsimonious Matrix-Variate FMR Maximum Likelihood Estimation Computational and Operative Details 3 Data Analyses Simulated Data Real Data 4 Conclusions References Robust Multivariate Modelling for Heterogeneous Data Sets with Mixtures of Multivariate Skew Laplace Normal Distributions 1 Introduction 2 The MSLN Distribution 3 Finite Mixtures of the MSLN Distributions ML Estimation Initial Values The Empirical Information Matrix 4 Applications Simulation Study An Illustrative Real Data Example: Old Faithful Geyser Data Set 5 Conclusions References Robust Estimation Through Preliminary Testing Based on the LAD-LASSO 1 Introduction 2 LAD-LASSO Estimator 3 Improvement Strategy on LAD 4 Numerical Study Synthetic Data Analysis Gross Domestic Product Data Analysis 5 Codes 6 Conclusion References