Correlation and dependence

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