In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Statistical Inference: The Minimum Distance Approach comprehensively overviews developments in density-based minimum distance inference for independently and identically distributed data. Extensions to other more complex models are also discussed.
Comprehensively covering the basics and applications of minimum distance inference, this book introduces and discusses: * The estimation and hypothesis testing problems for both discrete and continuous models * The robustness properties and the structural geometry of the minimum distance methods * The inlier problem and its possible solutions, and the weighted likelihood estimation problem * The extension of the minimum distance methodology in interdisciplinary areas, such as neural networks and fuzzy sets, as well as specialized models and problems, including semi-parametric problems, mixture models, grouped data problems, and survival analysis. Statistical Inference: The Minimum Distance Approach gives a thorough account of density-based minimum distance methods and their use in statistical inference. It covers statistical distances, density-based minimum distance methods, discrete and continuous models, asymptotic distributions, robustness, computational issues, residual adjustment functions, graphical descriptions of robustness, penalized and combined distances, weighted likelihood, and multinomial goodness-of-fit tests.
This carefully crafted resource is useful to researchers and scientists within and outside the statistics arena.
Indian Statistical Institute, Kolkata, India Muroran Institute of Technology, Muroran, Japan Clemson University, Clemson, SC, USA
Introduction General Notation Illustrative Examples Some Background and Relevant Definitions Parametric Inference based on the Maximum Likelihood Method Hypothesis Testing by Likelihood Methods Statistical Functionals and Influence Function Outline of the Book Statistical Distances Introduction Distances Based on Distribution Functions Density-Based Distances Minimum Hellinger Distance Estimation: Discrete Models Minimum Distance Estimation Based on Disparities: Discrete Models Some Examples Continuous Models Introduction Minimum Hellinger Distance Estimation Estimation of Multivariate Location and Covariance A General Structure The Basu-Lindsay Approach for Continuous Data Examples Measures of Robustness and Computational Issues The Residual Adjustment Function The Graphical Interpretation of Robustness The Generalized Hellinger Distance Higher Order Influence Analysis Higher Order Influence Analysis: Continuous Models Asymptotic Breakdown Properties The alpha-Influence Function Outlier Stability of Minimum Distance Estimators Contamination Envelopes The Iteratively Reweighted Least Squares (IRLS) The Hypothesis Testing Problem Disparity Difference Test: Hellinger Distance Case Disparity Difference Tests in Discrete Models Disparity Difference Tests: The Continuous Case Power Breakdown of Disparity Difference Tests Outlier Stability of Hypothesis Tests The Two Sample Problem Techniques for Inlier Modification Minimum Distance Estimation: Inlier Correction in Small Samples Penalized Distances Combined Distances o-Combined Distances Coupled Distances The Inlier-Shrunk Distances Numerical Simulations and Examples Weighted Likelihood Estimation The Discrete Case The Continuous Case Examples Hypothesis Testing Further Reading Multinomial Goodness-of-fit Testing Introduction Asymptotic Distribution of the Goodness-of-Fit Statistics Exact Power Comparisons in Small Samples Choosing a Disparity to Minimize the Correction Terms Small Sample Comparisons of the Test Statistics Inlier Modified Statistics An Application: Kappa Statistics The Density Power Divergence The Minimum L2 Distance Estimator The Minimum Density Power Divergence Estimator A Related Divergence Measure The Censored Survival Data Problem The Normal Mixture Model Problem Selection of Tuning Parameters Other Applications of the Density Power Divergence Other Applications Censored Data Minimum Hellinger Distance Methods in Mixture Models Minimum Distance Estimation Based on Grouped Data Semiparametric Problems Other Miscellaneous Topics Distance Measures in Information and Engineering Introduction Entropies and Divergences Csiszar's f-Divergence The Bregman Divergence Extended f-Divergences Additional Remarks Applications to Other Models Introduction Preliminaries for Other Models Neural Networks Fuzzy Theory Phase Retrieval Summary
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