Statistical Data Fusion

by Benjamin Kedem, Victor De Oliveira, Michael Sverchkov

Overview

'The book provides a comprehensive review of the DRM approach to data fusion. It is well written and easy to follow, although the technical details are not trivial. The authors did an excellent job in making a concise introduction of the statistical techniques in data fusion. The book contains several real data … Overall, I found that the book covers an important topic and the DRM is a promising tool in this area. Researchers on data fusion will surely find this book very helpful and I will use this book in studying with my PhD students.'
Journal of the American Statistical AssociationThis book comes up with estimates or decisions based on multiple data sources as opposed to more narrowly defined estimates or decisions based on single data sources. And as the world is awash with data obtained from numerous and varied processes, there is a need for appropriate statistical methods which in general produce improved inference by multiple data sources.The book contains numerous examples useful to practitioners from genomics. Topics range from sensors (radars), to small area estimation of body mass, to the estimation of small tail probabilities, to predictive distributions in time series analysis.

Product Details

ISBN-13:	9789813200180
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	03/20/2017
Pages:	200
Product dimensions:	6.60(w) x 10.00(h) x 0.60(d)

Table of Contents

Preface vii

1 Introduction 1

1.1 A Reference Distribution and its Distortions 2

1.1.1 A General Problem 11

2 Weighted Systems of Distributions 15

2.1 Simple Weighted Systems 15

2.1.1 Some Properties 16

2.2 Inference for Simple Weighted Systems 17

2.2.1 Empirical Distribution 17

2.2.2 Empirical Likelihood 18

2.2.3 Semiparametric Inference for Simple Weighted Systems 20

2.2.4 Specifying the Tilt Function 25

2.2.5 Mean Estimation 26

2.2.6 Testing Equidistribution 27

2.2.7 Application to Radar Meteorology 30

2.2.8 Discussion and Complements 36

2.3 Inference for General Weighted Systems 38

2.3.1 Hypothesis Testing 39

2.3.2 Application to Microarray Data 41

2.4 Appendix 44

2.4.1 Derivation of p_i from the Empirical Likelihood 44

2.4.2 Derivation of S, Λ 47

2.4.3 R Code for m = 2, h(x) = (x, x²) 49

3 Multivariate Extension 55

3.1 Introduction 55

3.2 The Bivariate Case 56

3.2.1 Case-Control Application 59

3.3 The General Multivariate Case 61

3.3.1 Kernel Density Estimation Using Fused Data 64

3.3.2 Bandwidth selection for gi 67

3.4 Semiparametric Regression 69

3.4.1 Case-Control Application 70

3.4.2 Marginalized Empirical Likelihood 71

4 Some Asymptotic Results 77

4.1 Weak Convergence of √n(G(t) - G(t)) 79

4.2 Goodness of Fit 82

4.2.1 Examples of Goodness of Fit 85

4.3 Appendix 86

4.3.1 Representation of Σ 86

4.3.2 Proof of Theorem 4.1.3 88

5 Out of Sample Fusion 91

5.1 Introduction 91

5.2 Normal or Not? 93

5.3 TS Prediction by Out of Sample Fusion 94

5.3.1 Mortality Prediction 95

5.3.2 Southern Oscillation Index Prediction 96

5.3.3 Unemployment Insurance Weekly Claims 100

5.3.4 Forecasting Mortality Rates 103

5.3.5 Application to VaR Estimation 106

5.4 Interval Estimation of Small Tail Probabilities 108

5.4.1 Confidence Intervals for Tail Probabilities 109

5.4.2 Repeated Out of Sample Fusion (ROSF) 110

5.4.3 Illustration of ROSF 113

6 Bayesian Weighted Systems 119

6.1 Introduction 119

6.2 Simple Weighted Systems of Distributions 121

6.2.1 Likelihood 122

6.2.2 Prior 123

6.3 Posterior Simulation 126

6.4 Bayesian Inference 130

6.4.1 Estimation 130

6.4.2 Example: Radar Meteorology 131

6.4.3 Test of Hypotheses 134

6.4.4 Example: Radar Meteorology (Continuation) 138

6.5 Discussion 139

7 Small Area Estimation 141

7.1 Sample and Sample-Complement Distributions 144

7.2 Optimal Small Area Predictors 147

7.3 Predictor Bias: Ignoring Informative Sampling 148

7.4 Prediction of Small Area Means 150

7.4.1 Noninformative Selection of Areas; within Areas 150

7.4.2 Informative Selection withing Areas; all Selected 152

7.4.3 Informative Selection: Predict Sampled Areas 154

7.4.4 Informative Selection: Predict Nonsampled Areas 157

7.5 Testing for Prediction Bias 160

7.5.1 Ignoring the Selection of Areas 160

7.5.2 Ignoring Sampling within the Areas 161

7.6 Estimating Mean Body Mass 162

7.7 Appendix: Informative Nonresponse 167

References 173

Index 185