Robust statistics for signal processing / Abdelhak M. Zoubir, Visa Koivunen, Esa Ollila, Michael Muma.

Format:

Book

Author/Creator:

Zoubir, Abdelhak M., author.

Koivunen, Visa, author.

Ollila, Esa, 1974- author.

Muma, Michael, 1981- author.

Language:

English

Subjects (All):

Robust statistics.

Signal processing--Mathematics.

Signal processing.

Physical Description:

1 online resource (xxii, 291 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2018.

Summary:

Understand the benefits of robust statistics for signal processing with this authoritative yet accessible text. The first ever book on the subject, it provides a comprehensive overview of the field, moving from fundamental theory through to important new results and recent advances. Topics covered include advanced robust methods for complex-valued data, robust covariance estimation, penalized regression models, dependent data, robust bootstrap, and tensors. Robustness issues are illustrated throughout using real-world examples and key algorithms are included in a MATLAB Robust Signal Processing Toolbox accompanying the book online, allowing the methods discussed to be easily applied and adapted to multiple practical situations. This unique resource provides a powerful tool for researchers and practitioners working in the field of signal processing.

Contents:

Cover

Half-title

Title page

Copyright information

Contents

Preface

Abbreviations

List of Symbols

1 Introduction and Foundations

1.1 History of Robust Statistics

1.2 Robust M-estimators for Single-Channel Data

1.2.1 Location and Scale Estimation

Maximum Likelihood Estimation of Location and Scale

M-estimation of Location and Scale

1.3 Measures of Robustness

1.3.1 The Influence Function and Qualitative Robustness

Sensitivity Curve

The Influence Function

Qualitative Robustness of an Estimator

1.3.2 The Breakdown Point and Quantitative Robustness

The Breakdown Point

The Maximum-Bias Curve

1.4 Concluding Remarks

2 Robust Estimation: The Linear Regression Model

2.1 Complex Derivatives and Optimization

2.2 The Linear Model and Organization of the Chapter

2.3 The Least Squares Estimator

2.4 Least Absolute Deviation and Rank-Least Absolute Deviation Regression

2.4.1 Simple Linear Regression without an Intercept

Weighted Median Regression: The Real-Valued Case

Weighted Median Regression: The Complex-Valued Case

2.4.2 Simple Linear Regression with Intercept

2.4.3 Computation of Least Absolute Deviation and Rank-Least Absolute Deviation Estimates

2.5 ML- and M-estimates of Regression with an Auxiliary Scale Estimate

2.5.1 Objective Function Approach vs. Estimating Equation Approach

2.5.2 Examples of Loss Functions

2.5.3 Computation Using the Iteratively Reweighted Least Squares Algorithm

2.6 Joint M-estimation of Regression and Scale Using Huber's Criterion

2.6.1 Minimization-Majorization Algorithm

2.6.2 Minimization-Majorization Algorithm for Huber's Criterion

2.7 Measures of Robustness

2.7.1 Outliers in the Linear Regression Model

2.7.2 (p+1)-dimensional Influence Function

2.7.3 Breakdown Point.

2.8 Positive Breakdown Point Regression Estimators

2.8.1 Least-Median of Squares and Least Trimmed Squares Estimator

2.8.2 S-Estimators and τ-Estimators

2.8.3 MM-Estimators

2.9 Simulation Studies

2.9.1 Study 1: Randomly Flipped Measurements

2.9.2 Study 2: Localization of Mobile User Equipment

2.10 Concluding Remarks

3 Robust Penalized Regression in the Linear Model

3.1 Sparse Regression and Outline of the Chapter

3.2 Extensions of the Lasso Penalty

3.3 The Lasso and the Elastic Net

3.3.1 Simple Linear Regression and Soft-Thresholding

3.3.2 Subgradient Equations for the Lasso/Elastic Net

3.3.3 Computation of the Lasso/Elastic Net

Cyclic Coordinate Descent Algorithm

Pathwise Coordinate Descent

3.4 The Least Absolute Deviation-Lasso and the Rank-Lasso

3.4.1 Simple Linear Regression (p = 1)

3.4.2 The Computation of Least Absolute Deviation-Lasso and Rank-Lasso Estimates: p > 1 Case

3.4.3 The Fused Rank-Lasso

Image Denoising Example

3.5 Joint Penalized M-estimation of Regression and Scale

3.5.1 Algorithm

3.6 Penalty Parameter Selection

3.7 Application Example: Prostate Cancer

3.8 Concluding Remarks

4 Robust Estimation of Location and Scatter (Covariance) Matrix

4.1 Complex Vector Space Isomorphism and Complex Distributions

4.2 Elliptically Symmetric Distributions

4.2.1 Real Elliptically Symmetric Distributions

4.2.2 Complex Elliptically Symmetric Distributions

4.2.3 Related Model: The Angular Central Gaussian Distribution

4.3 ML- and M-estimation of the Scatter Matrix

4.4 Examples of M- and ML-estimators

4.4.1 t[sub(ν)]M-estimator

4.4.2 Huber's Loss Function

4.4.3 Tyler's Loss Function

4.5 Regularized M-estimators of the Scatter Matrix

4.6 Signal Detection Application

4.6.1 Simulation Study

4.7 Concluding Remarks.

5 Robustness in Sensor Array Processing

5.1 Introduction

5.2 Basic Array Signal Model

5.3 Uncertainties in the Array Signal Model

5.3.1 Sources of Uncertainty

5.3.2 Robustness and Signal Model Errors

5.4 Statistically Robust Methods

5.4.1 Characterizing Robustness in Array Processing

Quantitative Robustness

Qualitative Robustness

5.4.2 Robust Procedures

Nonparametric Statistics

M-Estimation

Stochastic Maximum Likelihood

5.5 Array Processing Examples

5.6 Concluding Remarks

6 Tensor Models and Robust Statistics

6.1 Introduction

6.2 Tensor Notation and Basic Operations

6.3 Tensor Decompositions

6.4 Robust Tensor Decomposition

6.5 Combining Robustness with Sparsity

6.6 Simulation Examples

6.7 Concluding Remarks

7 Robust Filtering

7.1 Robust Wiener Filtering

7.1.1 Wiener Filtering

7.1.2 Robust Wiener Filtering

7.2 Nonparametric Nonlinear Robust Filters

7.3 Robust Kalman Filtering

7.3.1 3σ-Rejection and Score Function Type Kalman Filter

7.3.2 The Masreliez Approximate Conditional Mean Filter for Additive Outliers

7.3.3 The Masreliez Approximate Conditional Mean Filter for Innovation Outliers

7.3.4 The Schick and Mitter Approximate Conditional Mean Filter for Additive Outliers

7.3.5 Robust Regression-Based Kalman Filter

7.4 Robust Extended Kalman Filtering

7.4.1 Robust Extended Kalman Filter for the Tracking of Mobile User Equipment

7.5 Concluding Remarks

8 Robust Methods for Dependent Data

8.1 Signal and Outlier Models

8.1.1 Autoregressive Moving-Average Models

8.1.2 Outlier Models

8.2 Propagation of Outliers

8.2.1 Robust Approximate Conditional Mean Type Filters

8.2.2 Bounded Influence Propagation Model

8.3 An Overview of Robust Autoregressive Moving-Average Parameter Estimators

8.3.1 M-Estimation

8.3.2 S-Estimation.

8.3.3 MM-Estimation

8.3.4 τ-Estimation

8.3.5 Robust Autocorrelation-Based Estimators

8.3.6 Other Estimators

8.4 Robust Model Order Selection

8.5 Measures of Robustness

8.5.1 Influence Function for Dependent Data

8.5.2 Maximum Bias Curve for Dependent Data

8.5.3 Breakdown Point for Dependent Data

8.6 Algorithms

8.6.1 Computing BIP-AR(p) or Filtered AR(p) τ- (or S-Estimates) Based on a Robust Levinson-Durbin Procedure

8.6.2 Algorithms for Computing MA(q) and ARMA(p,q) Parameter Estimates

Robust Starting Point Algorithm

8.6.3 Simulation and Real-Data Examples

8.7 Concluding Remarks

9 Robust Spectral Estimation

9.1 Robust Nonparametric Spectral Estimation

9.1.1 Robust-Averaging-Based Nonparametric Estimators

9.1.2 The M-Periodogram and the [ell[sub(p)]]-Periodogram

9.1.3 The Biweight Robust Fourier Transform

9.2 Autoregressive Moving-Average Model-Based Robust Parametric Spectral Estimation

9.3 Simulation Example: Robust Spectral Estimation

9.4 Robust Subspace-Based Frequency Estimation

9.5 Concluding Remarks

10 Robust Bootstrap Methods

10.1 Introduction

10.1.1 What Is the Bootstrap?

10.1.2 The Problem When Using the Bootstrap for Robust Estimators

10.2 Existing Robust Bootstrap Methods

10.2.1 The Influence Function Bootstrap

10.2.2 The Stratified Bootstrap

10.2.3 The Fast and Robust Bootstrap

10.2.4 The Robust Starting Point Bootstrap

10.3 Robust Bootstrap Confidence Interval Estimation in Linear Regression

10.3.1 Breakdown of Confidence Intervals

Maximum-Bias and Interval Length Curves

Empirical Coverage Probability

Connection between Confidence Interval Bias, Length and Empirical Coverage Probability

10.3.2 Comparison of Robust Bootstrap Methods

Simulation Setup

Simulation Results.

10.4 Robust and Scalable Bootstrap for Large-Scale Data

10.4.1 Introduction

10.4.2 Making the Bootstrap Method Scalable

10.4.3 A Fast, Robust, and Scalable Bootstrap Method

10.4.4 MM-estimation Equations in the Bag of Little Fast and Robust Bootstraps Method

10.4.5 Simulation Example

10.4.6 Million Song Data Set Example

10.5 Concluding Remarks

11 Real-Life Applications

11.1 Localization of User Equipment in an Indoor Environment

11.2 Blood Glucose Concentration in Photometric Handheld Devices

11.3 European Tracer Experiment Source Estimation

Performance Metrics

11.4 Robust Short-Term Load Forecasting

11.5 Robust Data Cleaning for Photoplethysmography-Based Pulse-Rate Variability Analysis

Bibliography

Index.

Notes:

Title from publisher's bibliographic system (viewed on 29 Oct 2018).

Includes bibliographical references and index.

ISBN:

1-108-68048-8

1-139-08429-1

1-108-58275-3

OCLC:

1060524627