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Combinatorial Inference in Geometric Data Analysis [Kõva köide]

(Coheris Spad, Suresnes, France), (Université Paris 13, Villetaneuse, France), (MAP5 - Université Paris Descartes, France)
  • Formaat: Hardback, 256 pages, kõrgus x laius: 234x156 mm, kaal: 550 g, 27 Tables, black and white; 122 Line drawings, black and white; 23 Halftones, black and white; 145 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Computer Science & Data Analysis
  • Ilmumisaeg: 22-Feb-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1498781616
  • ISBN-13: 9781498781619
Teised raamatud teemal:
Combinatorial Inference in Geometric Data AnalysisSuurem pilt
  • Formaat: Hardback, 256 pages, kõrgus x laius: 234x156 mm, kaal: 550 g, 27 Tables, black and white; 122 Line drawings, black and white; 23 Halftones, black and white; 145 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Computer Science & Data Analysis
  • Ilmumisaeg: 22-Feb-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1498781616
  • ISBN-13: 9781498781619
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781498781619.html
Märksõnad:
Geometric Data Analysis designates the approach of Multivariate Statistics that conceptualizes the set of observations as a Euclidean cloud of points. Combinatorial Inference in Geometric Data Analysis gives an overview of multidimensional statistical inference methods applicable to clouds of points that make no assumption on the process of generating data or distributions, and that are not based on random modelling but on permutation procedures recasting in a combinatorial framework.

It focuses particularly on the comparison of a group of observations to a reference population (combinatorial test) or to a reference value of a location parameter (geometric test), and on problems of homogeneity, that is the comparison of several groups for two basic designs. These methods involve the use of combinatorial procedures to build a reference set in which we place the data. The chosen test statistics lead to original extensions, such as the geometric interpretation of the observed level, and the construction of a compatibility region.

Features:











Defines precisely the object under study in the context of multidimensional procedures, that is clouds of points





Presents combinatorial tests and related computations with R and Coheris SPAD software





Includes four original case studies to illustrate application of the tests





Includes necessary mathematical background to ensure it is selfcontained

This book is suitable for researchers and students of multivariate statistics, as well as applied researchers of various scientific disciplines. It could be used for a specialized course taught at either master or PhD level.
Preface vii
Symbols xi
1 Introduction
1(8)
1.1 On Combinatorial Inference
1(3)
1.2 On Geometric Data Analysis
4(1)
1.3 On Inductive Data Analysis
5(1)
1.4 Computational Aspects
6(3)
2 Cloud of Points in a Geometric Space
9(20)
2.1 Basic Statistics
10(4)
2.2 Covariance Structure of a Cloud
14(6)
2.3 Mahalanobis Distance and Principal Ellipsoids
20(5)
2.4 Partition of a Cloud
25(4)
3 Combinatorial Typicality Tests
29(36)
3.1 The Typicality Problem
29(3)
3.2 Combinatorial Typicality Test for Mean Point
32(13)
3.3 One-dimensional Case: Typicality Test for Mean
45(4)
3.4 Combinatorial Typicality Test for Variance
49(2)
3.5 Combinatorial Inference in GDA
51(4)
3.6 Computations with R and Coheris SPAD Software
55(10)
4 Geometric Typicality Test
65(42)
4.1 Principle of the Test
65(4)
4.2 Geometric Typicality Test for Mean Point
69(17)
4.3 One-dimensional Case: Typicality for Mean
86(4)
4.4 The Case of a Design with Two Repeated Measures
90(2)
4.5 Other Methods
92(5)
4.6 Computations with R and Coheris SPAD Software
97(10)
5 Homogeneity Permutation Tests
107(46)
5.1 The Homogeneity Problem
107(1)
5.2 Principle of Combinatorial Homogeneity Tests
108(1)
5.3 Homogeneity of Independent Groups: General Case
109(7)
5.4 Homogeneity of Two Independent Groups
116(17)
5.5 The Case of a Repeated Measures Design
133(7)
5.6 Other Methods
140(1)
5.7 Computations with R and Coheris SPAD Software
141(12)
6 Research Case Studies
153(68)
6.1 The Parkinson Study
156(14)
6.2 The Members of French Parliament and Globalisation in 2006
170(18)
6.3 The European Central Bankers Study
188(12)
6.4 Cognitive Tests and Education
200(21)
7 Mathematical Bases
221(24)
7.1 Matrix Calculus
222(2)
7.2 Finite-Dimensional Vector Space
224(5)
7.3 Euclidean Vector Space
229(7)
7.4 Multidimensional Geometry
236(5)
7.5 Orthogonal Projection
241(4)
Bibliography 245(5)
Author Index 250(2)
Subject Index 252
Brigitte Le Roux is associate researcher at Laboratoire de Mathématiques Appliquées (MAP5/CNRS) of the Paris Descartes university and at the political research center of Sciences-Po Paris (CEVIPOF/CNRS). She completed her doctoral dissertation in applied mathematics at the Faculté des Sciences de Paris in 1970 that was supervised by Jean-Paul Benzécri. She has contributed to numerous theoretical research works and full scale empirical studies involving Geometric Data Analysis. She has authored and co-authored nine books, especially on Geometric Data Analysis (2004, Kluwer Academic Publishers) and Multiple Correspondence Analysis (2010, QASS series of Sage publications, n° 163).

Solène Bienaise is data scientist at Coheris (company). She completed her doctoral dissertation in applied mathematics in 2013 at the Paris Dauphine University, under the direction of Pierre Cazes and Brigitte Le Roux.

Jean-Luc Durand is associate professor at the Psychology department and researcher at LEEC (Laboratoire dEthologie Expérimentale et Comparée) of Paris 13 University. He completed his doctoral dissertation in Psychology at Paris Descartes University in 1989, supervised by Henry Rouanet. He teaches statistical methodology in psychology and ethology.