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.
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