Innovations in Multivariate Statistical Modeling: Navigating Theoretical and Multidisciplinary Domains

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