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This series of books collects a diverse array of work that provides the reader with theoretical and applied information on data analysis methods, models, and techniques, along with appropriate applications. Volume 1 begins with an introductory chapter by Gilbert Saporta, a leading expert in the field, who summarizes the developments in data analysis over the last 50 years. The book is then divided into three parts: Part 1 presents clustering and regression cases; Part 2 examines grouping and decomposition, GARCH and threshold models, structural equations, and SME modeling; and Part 3 presents symbolic data analysis, time series and multiple choice models, modeling in demography, and data mining.
Autorentext
Christos H. Skiadas is the Founder and former Director of the Data Analysis and Forecasting Laboratory at the Technical University of Crete, Greece. He continues his work at the university at the ManLab in the Department of Production Engineering and Management.
James R. Bozeman holds a PhD in Mathematics from Dartmouth College, USA, and is Professor of Mathematics at the American University of Malta.
Inhalt
Preface xi
Introduction xv
Gilbert SAPORTA
Part 1 Clustering and Regression 1
Chapter 1 Cluster Validation by Measurement of Clustering Characteristics Relevant to the User **3
**Christian HENNIG
1.1 Introduction 3
1.2 General notation 5
1.3 Aspects of cluster validity 6
1.3.1 Small within-cluster dissimilarities 6
1.3.2 Between-cluster separation 7
1.3.3 Representation of objects by centroids 7
1.3.4 Representation of dissimilarity structure by clustering 8
1.3.5 Small within-cluster gaps 9
1.3.6 Density modes and valleys 9
1.3.7 Uniform within-cluster density 12
1.3.8 Entropy 12
1.3.9 Parsimony 13
1.3.10 Similarity to homogeneous distributional shapes 13
1.3.11 Stability 13
1.3.12 Further Aspects 14
1.4 Aggregation of indexes 14
1.5 Random clusterings for calibrating indexes 15
1.5.1 Stupid K-centroids clustering 16
1.5.2 Stupid nearest neighbors clustering 16
1.5.3 Calibration 17
1.6 Examples 18
1.6.1 Artificial data set 18
1.6.2 Tetragonula bees data 20
1.7 Conclusion 22
1.8 Acknowledgment 23
1.9 References 23
Chapter 2 Histogram-Based Clustering of Sensor Network Data **25
**Antonio BALZANELLA and Rosanna VERDE
2.1 Introduction 25
2.2 Time series data stream clustering 28
2.2.1 Local clustering of histogram data 30
2.2.2 Online proximity matrix updating 32
2.2.3 Off-line partitioning through the dynamic clustering algorithm for dissimilarity tables 33
2.3 Results on real data 34
2.4 Conclusions 36
2.5 References 36
Chapter 3 The Flexible Beta Regression Model **39
**Sonia MIGLIORATI, Agnese MDI BRISCO and Andrea ONGARO
3.1 Introduction 39
3.2 The FB distribution 41
3.2.1 The beta distribution 41
3.2.2 The FB distribution 41
3.2.3 Reparameterization of the FB 42
3.3 The FB regression model 43
3.4 Bayesian inference 44
3.5 Illustrative application 47
3.6 Conclusion 48
3.7 References 50
Chapter 4 S-weighted Instrumental Variables **53
**Jan Ámos VÍEK
4.1 Summarizing the previous relevant results 53
4.2 The notations, framework, conditions and main tool 55
4.3 S-weighted estimator and its consistency 57
4.4 S-weighted instrumental variables and their consistency 59
4.5 Patterns of results of simulations 64
4.5.1 Generating the data 65
4.5.2 Reporting the results 66
4.6 Acknowledgment 69
4.7 References 69
Part 2 Models and Modeling 73
Chapter 5 Grouping Property and Decomposition of Explained Variance in Linear Regression **75
**Henri WALLARD
5.1 Introduction 75
5.2 CAR scores 76
5.2.1 Definition and estimators 76
5.2.2 Historical criticism of the CAR scores 79
5.3 Variance decomposition methods and SVD 79
5.4 Grouping property of variance decomposition methods 80
5.4.1 Analysis of grouping property for CAR scores 81
5.4.2 Demonstration with two predictors 82
5.4.3 Analysis of grouping property using SVD 83
5.4.4 Application to the diabetes data set 86
5.5 Conclusions 87
5.6 References 88
Chapter 6 On GARCH Models with Temporary Structural Changes **91
**Norio WATANABE and Fumiaki OKIHARA
6.1 Introduction...