Correlation and dependence

(Imperial College Press) A graduate text on correlation and dependence concepts and measures, designed to help remedy the lack of such texts for students in statistics, engineering, and mathematics. Takes a tour of this neglected subject, requiring some background in mathematical statistics and integral calculus. DLC: Correlation (Statistics). Contents......Page 10 Preface......Page 8 1.1 Notations......Page 18 1.2 Definitions......Page 20 2.1 Independence......Page 24 2.2 Zero Correlation Versus Dependence......Page 27 2.3 Some Geometrical Examples......Page 35 2.4 Some Further Historical Remarks......Page 39 2.5 A Brief Tour of Early Applications and Misinterpretations......Page 42 3.1 Introduction......Page 48 3.2 Concepts of Positive Dependence......Page 50 3.3 Negative Dependence for More than Two Variables......Page 60 3.4 Setwise Dependence......Page 67 3.5 Other Approaches......Page 70 3.6 Positive Dependence Orderings......Page 71 3.7 Bayesian Approach to Stochastic Dependence......Page 80 4.1 Introduction......Page 82 4.2 Definition and Some Properties......Page 83 4.3 The Frechet Bounds......Page 85 4.4 Examples......Page 87 4.5 Construction of a Copula......Page 90 4.6 Archimedean Copulas......Page 101 4.7 Archimax Copulas......Page 111 4.8 Copulas with Discontinuity Constraints......Page 113 4.9 Copulas with More than Two Variables......Page 118 4.10 Simulation Procedures......Page 127 5.1 Introduction......Page 130 5.2 Initial Definition......Page 131 5.3 Regression and Correlation......Page 132 5.4 Iterations......Page 134 5.6 A Class of n-variate FGM Distributions......Page 136 5.7 Further Extensions......Page 147 5.8 FGM Sequences......Page 158 6.1 Introduction......Page 166 6.2 Global Measures of Dependence......Page 167 6.3 Local Indices of Dependence......Page 188 6.4 Non-parametric Estimation of Local Indices......Page 207 6.5 A Search for the Localisation of the Maximal Association......Page 211 Bibliography......Page 220 Index......Page 234 The concept of dependence permeates the Earth and its inhabitants in a most profound manner. Examples of interdependent meteorological phenomena in nature and interdependence in the medical, social, and political aspects of our existence, not to mention the economic structures, are too numerous to be cited individually. Moreover, the dependence is obviously not deterministic but of a stochastic nature. However, it seems that none of the departments of statistics, engineering, economics and mathematics in the academic institutions throughout the world offer courses dealing with dependence concepts and measures.This book can thus be viewed as an attempt to remedy the situation, and it has been written for a graduate course or a seminar on correlation and dependence concepts and measures. A modest background in mathematical statistics and probability and integral calculus is required. The book is not a full-scale expedition up another statistical Alp. Rather, it is a tour over a somewhat neglected but important terrain. The chapter on correlation is written for a layman. The concept of dependence permeates the Earth and its inhabitants in a most profound manner. Examples of interdependent meteorological phenomena in nature and interdependence in the medical, social, and political aspects of our existence, not to mention the economic structures, are too numerous to be cited individually. Moreover, the dependence is obviously not deterministic but of a stochastic nature. However, it seems that none of the departments of statistics, engineering, economics and mathematics in the academic institutions throughout the world offer courses dealing with dependence concepts and measures. This book can thus be viewed as an attempt to remedy the situation, and it has been written for a graduate course or a seminar on correlation and dependence concepts and measures. A modest background in mathematical statistics and probability and integral calculus is required. The book is not a full-scale expedition up another statistical Alp. Rather, it is a tour over a somewhat neglected but important terrain. The chapter on correlation is written for a layman (1) Cm (E) is the place of the real valued functions, defined on E with a continuous m-th derivative.