Robust correlation : theory and applications /: theory and applications. (2016)

• Record Type: Book
• Further Information: Note: Georgy L. Shevlyakov, Hannu Oja.
• Authors: Shevlyakov, Georgy L; Oja, Hannu
• Contents: Preface xi 1 Introduction 1 1.1 Historical Remarks 1 1.2 Ontological Remarks 4 References 7 2 Classical Measures of Correlation 9 2.1 Preliminaries 9 2.2 Pearson’s Correlation Coefficient: Definitions and Interpretations 11 2.3 Nonparametric Measures of Correlation 23 2.4 Informational Measures of Correlation 28 2.5 Summary 29 References 30 3 Robust Estimation of Location 33 3.1 Preliminaries 33 3.2 Huber’s Minimax Approach 35 3.3 Hampel’s Approach Based on Influence Functions 46 3.4 Robust Estimation of Location: a Sequel 55 3.5 Stable Estimation 71 3.6 Robustness Versus Gaussianity 82 3.7 Summary 98 References 99 4 Robust Estimation of Scale 103 4.1 Preliminaries 103 4.2 M- and L-Estimates of Scale 107 4.3 Huber Minimax Variance Estimates of Scale 112 4.4 Highly Efficient Robust Estimates of Scale 115 4.5 Monte Carlo Experiment 125 4.6 Summary 133 References 133 5 Robust Estimation of Correlation Coefficients 135 5.1 Preliminaries 135 5.2 Main Groups of Robust Estimates of the Correlation Coefficient 136 5.3 Asymptotic Properties of the Classical Estimates of the Correlation Coefficient 142 5.4 Asymptotic Properties of Nonparametric Estimates of Correlation 145 5.5 Bivariate Independent Component Distributions 148 5.6 Robust Estimates of the Correlation Coefficient Based on Principal Component Variances 151 5.7 Robust Minimax Bias and Variance Estimates of the Correlation Coefficient 155 5.8 Robust Correlation via Highly Efficient Robust Estimates of Scale 157 5.9 Robust M-Estimates of the Correlation Coefficient in Independent Component Distribution Models 158 5.10 Monte Carlo Performance Evaluation 161 5.11 Robust Stable Radical M-Estimate of the Correlation Coefficient of the Bivariate Normal Distribution 166 5.12 Summary 168 References 169 6 Classical Measures of Multivariate Correlation 171 6.1 Preliminaries 171 6.2 Covariance Matrix and Correlation Matrix 172 6.3 Sample mean vector and sample covariance matrix 174 6.4 Families of Multivariate Distributions 175 6.5 Asymptotic Behavior of Sample Covariance Matrix and Sample Correlation Matrix 179 6.6 First Uses of Covariance and Correlation Matrices 182 6.7 Working with the Covariance Matrix - Principal Component Analysis 183 6.8 Working with Correlations - Canonical Correlation Analysis 187 6.9 Conditionally Uncorrelated Components 191 6.10 Summary 191 References 192 7 Robust Estimation of Scatter and Correlation Matrices 193 7.1 Preliminaries 193 7.2 Multivariate Location and Scatter Functionals 193 7.3 Influence Functions and Asymptotics 195 7.4 M-functionals for Location and Scatter 198 7.5 Breakdown Point 201 7.6 Use of Robust Scatter Matrices 202 7.7 Further Uses of Location and Scatter Functionals 203 7.8 Summary 205 References 205 8 Nonparametric Measures of Multivariate Correlation 207 8.1 Preliminaries 207 8.2 Univariate signs and ranks 207 8.3 Marginal sign and ranks 210 8.4 Spatial signs and ranks 211 8.5 Affine equivariant signs and ranks 215 8.6 Summary 219 References 219 9 Applications to Exploratory Data Analysis: Detection of Outliers 221 9.1 Preliminaries 221 9.2 State of the Art 222 9.3 Problem Setting 227 9.4 A New Measure of Outlier Detection Performance 229 9.5 Robust Versions of the Tukey Boxplot with Their Application to Detection of Outliers 233 9.6 Robust Bivariate Boxplots and Their Performance Evaluation 235 9.7 Summary 242 References 243 10 Applications to Time Series Analysis: Robust Spectrum Estimation 245 10.1 Preliminaries 245 10.2 Classical Estimation of a Power Spectrum 246 10.3 Robust Estimation of a Power Spectrum 249 10.4 Performance Evaluation 253 10.5 Summary 259 References 259 11 Applications to Signal Processing: Robust Detection 261 11.1 Preliminaries 261 11.2 Robust Minimax Detection Based on a Distance Rule 264 11.3 Robust Detection of a Weak Signal with Redescending M-Estimates 273 11.4 A Unified Neyman-Pearson Detection of Weak Signals in a Fusion Model with Fading Channels and Non-Gaussian Noises 284 11.5 Summary 294 References 294 12 Final Remarks 297 12.1 Points of Growth: Open Problems in Multivariate Statistics 297 12.2 Points of Growth: Open Problems in Applications 298 Index 299
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 519.537; Correlation (Statistics)
• Languages: English
• ISBNs: 9781119264491; 9781119264538
• Related ISBNs: 9781118493458
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.