Table des matières

Preface

vii

Symbols

xi

Chapter 1. Introduction

1

1.1 On combinatorial inference

1

1.2 On Geometric Data Analysis

4

1.3 On Inductive Data Analysis

5

1.4 Compatational Aspects

6

2.1 Basic Statistics

10

2.2 Covariance Structure of a Cloud

14

2.3 Mahalanobis Distance an Principal Ellipsoids

20

2.4 Partition of a Cloud

25

3.1 The Typicality Problem

29

3.2 Combinatorial Typicality Test for Mean Point

32

3.3 One-dimensional Case: Typicality Test for Mean

45

3.4 Combinatorial Typicality Test for Variance

49

3.5 Combinatorial Inference in GDA

51

3.6 Computations with R and Coheris Spad Software

55

4.1 Principle of the Test

65

4.2 Geoemtric Typicality Test for Mean Point

69

4.3 One-dimensional Case: Typicality for Mean

86

4.4 The case of a Design with Two Repeated Measures

90

4.5 Other Methods

92

4.6 Computations with R and Coheris Spad Software

97

5.1 The Homogeneity Problem

107

5.2 Principle of Combinatorial Homogeneity Tests

108

5.3 Homogeneity of Independent Groups: General Case

109

5.4 Homogeneity of Two Independent Groups

116

5.5 The Case of a Repeated Measures Design

133

5.6 Other Methods

140

5.7 Computations with R and Coheris Spad Software

141

6.1 The Parkinson Study

156

6.2 The Members of French Parliament and Globalisation

170

6.3 The European Central Bankers Study

188

6.4 Cognitive Tests and Education

200