Robust Correlation: Theory and Applications

This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data. Key features: -Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields.-Focuses on implementation of methodology and application of robust correlation with R.-Introduces the main approaches in robust statistics, such as Huber's minimax approach and Hampel's approach based on influence functions.-Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates.-Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data.-Includes an accompanying website featuring computer code and datasets -Features exercises and examples throughout the text using both small and large data sets. Theoretical and applied statisticians, specialists in multivariate statistics, robust statistics, robust time series analysis, data analysis and signal processing will benefit from this book. Practitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful.

4.2 M- and L-Estimates of Scale.

Cover; Title Page; Copyright; Dedication; Contents; Preface; Acknowledgements; About the Companion Website; Chapter 1 Introduction; 1.1 Historical Remarks; 1.2 Ontological Remarks; 1.2.1 Forms of data representation; 1.2.2 Types of data statistics; 1.2.3 Principal aims of statistical data analysis; 1.2.4 Prior information about data distributions and related approaches to statistical data analysis; References; Chapter 2 Classical Measures of Correlation; 2.1 Preliminaries; 2.2 Pearson's Correlation Coefficient: Definitions and Interpretations; 2.2.1 Introductory remarks.

2.2.2 Correlation via regression2.2.3 Correlation via the coefficient of determination; 2.2.4 Correlation via the variances of the principal components; 2.2.5 Correlation via the cosine of the angle between the variable vectors; 2.2.6 Correlation via the ratio of two means; 2.2.7 Pearson's correlation coefficient between random events; 2.3 Nonparametric Measures of Correlation; 2.3.1 Introductory remarks; 2.3.2 The quadrant correlation coefficient; 2.3.3 The Spearman rank correlation coefficient; 2.3.4 The Kendall -rank correlation coefficient; 2.3.5 Concluding remark.

2.4 Informational Measures of Correlation2.…