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Robust Estimation and Hypothesis Testing 1st Edition by Moti L Tiku ISBN 8122425372 9788122425376

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Author(s): Moti L. Tiku
ISBN(s): 9788122425376, 8122425372
Edition: New Age
File Details: PDF, 2.24 MB
Year: 2004
Language: english
SKU: EB-1011266 Category: Tag:

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ISBN 10: 8122425372 
ISBN 13: 9788122425376
Author: Moti L Tiku

In statistical theory and practice, a certain distribution is usually assumed and then optimal solutions sought. Since deviations from an assumed distribution are very common, one cannot feel comfortable with assuming a particular distribution and believing it to be exactly correct. That brings the robustness issue in focus. In this book, we have given statistical procedures which are robust to plausible deviations from an assumed mode. The method of modified maximum likelihood estimation is used in formulating these procedures. The modified maximum likelihood estimators are explicit functions of sample observations and are easy to compute. They are asymptotically fully efficient and are as efficient as the maximum likelihood estimators for small sample sizes. The maximum likelihood estimators have computational problems and are, therefore, elusive. A broad range of topics are covered in this book. Solutions are given which are easy to implement and are efficient. The solutions are also robust to data anomalies: outliers, inliers, mixtures and data contaminations. Numerous real life applications of the methodology are given.

Robust Estimation and Hypothesis Testing 1st Table of contents:

Part I: Foundations of Robust Statistics

Chapter 1: Classical Estimation and Hypothesis Testing

  • 1.1 Overview of Estimation Theory

  • 1.2 Maximum Likelihood Estimation

  • 1.3 Classical Hypothesis Testing Framework

  • 1.4 Limitations under Model Deviations

Chapter 2: Concepts and Measures of Robustness

  • 2.1 Influence Functions

  • 2.2 Breakdown Point

  • 2.3 Sensitivity Curves

  • 2.4 Robustness Criteria for Estimators

Part II: Robust Estimation Techniques

Chapter 3: Location and Scale Estimators

  • 3.1 Median and Trimmed Means

  • 3.2 M-Estimators

  • 3.3 R-Estimators and L-Estimators

  • 3.4 Weighted and Winsorized Estimators

Chapter 4: Regression and Multivariate Estimation

  • 4.1 Robust Linear Regression

  • 4.2 Generalized Linear Models

  • 4.3 Robust Covariance and Multivariate Location

  • 4.4 High-Dimensional Robust Estimation

Chapter 5: Computational Methods in Robust Estimation

  • 5.1 Iterative Algorithms

  • 5.2 Numerical Convergence and Stability

  • 5.3 Software and Implementation Examples

Part III: Robust Hypothesis Testing

Chapter 6: Robust Tests for Location and Scale

  • 6.1 One-Sample and Two-Sample Problems

  • 6.2 Rank-Based Tests

  • 6.3 Sign Tests and Sign-Rank Tests

Chapter 7: Robust Tests in Regression and Multivariate Analysis

  • 7.1 Regression Coefficients

  • 7.2 Multivariate Location and Covariance

  • 7.3 Outlier Detection and Influence Analysis

Chapter 8: Asymptotic Theory for Robust Testing

  • 8.1 Asymptotic Distribution of Robust Estimators

  • 8.2 Efficiency and Robustness Trade-offs

  • 8.3 Robust Confidence Intervals

Part IV: Applications and Case Studies

Chapter 9: Practical Applications of Robust Methods

  • 9.1 Economics and Finance

  • 9.2 Engineering and Signal Processing

  • 9.3 Biostatistics and Epidemiology

  • 9.4 Environmental and Social Sciences

Chapter 10: Simulation Studies and Performance Evaluation

  • 10.1 Monte Carlo Studies

  • 10.2 Comparing Classical and Robust Procedures

  • 10.3 Guidelines for Choosing Robust Methods

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Tags: Moti L Tiku, Robust Estimation, Hypothesis Testing