Combinatorial inference in geometric data analysis

✍ Scribed by Bienaise, Solène; Durand, Jean-Luc; Le Roux, Brigitte

• Publisher: Chapman and Hall/CRC
• Year: 2019
• Tongue: English
• Leaves: 269
• Series: Chapman and Hall/CRC Computer Science and Data Analysis Ser
• Category: Library

✦ Synopsis

Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Symbols; 1: Introduction; 1.1 On Combinatorial Inference; 1.2 On Geometric Data Analysis; 1.3 On Inductive Data Analysis; 1.4 Computational Aspects; 2: Cloud of Points in a Geometric Space; 2.1 Basic Statistics; 2.2 Covariance Structure of a Cloud; 2.3 Mahalanobis Distance and Principal Ellipsoids; 2.4 Partition of a Cloud; 3: Combinatorial Typicality Tests; 3.1 The Typicality Problem; 3.2 Combinatorial Typicality Test for Mean Point; 3.3 One-dimensional Case: Typicality Test for Mean

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 8
Symbols......Page 12
1.1 On Combinatorial Inference......Page 14
1.2 On Geometric Data Analysis......Page 17
1.3 On Inductive Data Analysis......Page 18
1.4 Computational Aspects......Page 19
2: Cloud of Points in a Geometric Space......Page 22
2.1 Basic Statistics......Page 23
2.2 Covariance Structure of a Cloud......Page 27
2.3 Mahalanobis Distance and Principal Ellipsoids......Page 33
2.4 Partition of a Cloud......Page 38
3.1 The Typicality Problem......Page 42
3.2 Combinatorial Typicality Test for Mean Point......Page 45
3.3 One-dimensional Case: Typicality Test for Mean......Page 58
3.4 Combinatorial Typicality Test for Variance......Page 62
3.5 Combinatorial Inference in GDA......Page 64
3.6 Computations with R and Coheris SPAD Software......Page 68
4.1 Principle of the Test......Page 78
4.2 Geometric Typicality Test for Mean Point......Page 82
4.3 One-dimensional Case: Typicality for Mean......Page 99
4.4 The Case of a Design with Two Repeated Measures......Page 103
4.5 Other Methods......Page 105
4.6 Computations with R and Coheris SPAD Software......Page 110
5.1 The Homogeneity Problem......Page 120
5.2 Principle of Combinatorial Homogeneity Tests......Page 121
5.3 Homogeneity of Independent Groups: General Case......Page 122
5.4 Homogeneity of Two Independent Groups......Page 129
5.5 The Case of a Repeated Measures Design......Page 146
5.6 Other Methods......Page 153
5.7 Computations with R and Coheris SPAD Software......Page 154
6: Research Case Studies......Page 166
6.1 The Parkinson Study......Page 169
6.2 The Members of French Parliament and Globalisation in 2006......Page 183
6.3 The European Central Bankers Study......Page 201
6.4 Cognitive Tests and Education......Page 213
7: Mathematical Bases......Page 234
7.1 Matrix Calculus......Page 235
7.2 Finite-Dimensional Vector Space......Page 237
7.3 Euclidean Vector Space......Page 242
7.4 Multidimensional Geometry......Page 249
7.5 Orthogonal Projection......Page 254
Bibliography......Page 258
Author Index......Page 263
Subject Index......Page 265

✦ Subjects

Combinatorial analysis;Geometric analysis;Statistics;Electronic books