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Introduction to Multivariate Analysis: Linear and Nonlinear Modeling

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"Multivariate techniques are used to analyze data that arise from more than one variable in which there are relationships between the variables. Mainly based on the linearity of observed variables, these techniques are useful for extracting information and patterns from multivariate data as well as for the understanding the structure of random phenomena. This book describes the concepts of linear and nonlinear

Abstract: "Multivariate techniques are used to analyze data that arise from more than one variable in which there are relationships between the variables. Mainly based on the linearity of observed variables, these techniques are useful for extracting information and patterns from multivariate data as well as for the understanding the structure of random phenomena. This book describes the concepts of linear and nonlinear multivariate techniques, including regression modeling, classification, discrimination, dimension reduction, and clustering"--

"The aim of statistical science is to develop the methodology and the theory for extracting useful information from data and for reasonable inference to elucidate phenomena with uncertainty in various fields of the natural and social sciences. The data contain information about the random phenomenon under consideration and the objective of statistical analysis is to express this information in an understandable form using statistical procedures. We also make inferences about the unknown aspects of random phenomena and seek an understanding of causal relationships. Multivariate analysis refers to techniques used to analyze data that arise from multiple variables between which there are some relationships. Multivariate analysis has been widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Techniques would include regression, discriminant analysis, principal component analysis, clustering, etc., and are mainly based on the linearity of observed variables. In recent years, the wide availability of fast and inexpensive computers enables us to accumulate a huge amount of data with complex structure and/or high-dimensional data. Such data accumulation is also accelerated by the development and proliferation of electronic measurement and instrumentation technologies. Such data sets arise in various fields of science and industry, including bioinformatics, medicine, pharmaceuticals, systems engineering, pattern recognition, earth and environmental sciences, economics and marketing. "

Author(s): Konishi, Sadanori
Series: Texts in statistical science
Publisher: CRC Press
Year: 2014

Language: English
Pages: 338
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;

Content: Introduction Regression Modeling Classification and Discrimination Dimension Reduction Clustering Linear Regression Models Relationship between Two Variables Relationships Involving Multiple Variables Regularization Nonlinear Regression Models Modeling Phenomena Modeling by Basis Functions Basis Expansions Regularization Logistic Regression Models Risk Prediction Models Multiple Risk Factor Models Nonlinear Logistic Regression Models Model Evaluation and Selection Criteria Based on Prediction Errors Information Criteria Bayesian Model Evaluation Criterion Discriminant Analysis Fisher's Linear Discriminant Analysis Classification Based on Mahalanobis Distance Variable Selection Canonical Discriminant Analysis Bayesian Classification Bayes' Theorem Classification with Gaussian Distributions Logistic Regression for Classification Support Vector Machines Separating Hyperplane Linearly Nonseparable Case From Linear to Nonlinear Principal Component Analysis Principal Components Image Compression and Decompression Singular Value Decomposition Kernel Principal Component Analysis Clustering Hierarchical Clustering Nonhierarchical Clustering Mixture Models for Clustering Appendix A: Bootstrap Methods Appendix B: Lagrange Multipliers Appendix C: EM Algorithm Bibliography Index