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Statistical Inference
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Statistical distances have two very important uses in statistical analysis. Firstly, they can be applied naturally to the case of parametric statistical inference. The idea of minimum distance estimation has been around for a while and there are many nice properties that the minimum distance estimators enjoy. Minimum distance estimation was pioneered by Wolfowitz in the 1950s (1952, 1953, 1954, 1957). He studied minimum distance estimators as a class, looked at the large sample results, established their strong con- sistency under general conditions and considered the minimized distances in testing goodness-of-fit. Parr (1981) gives a comprehensive review of minimum distance methods up to that point. Vajda (1989) and Pardo (2006) have pro- vided useful treatments in statistical inference based on divergence measures.
The most important idea in parametric minimum distance estimation is the quantification of the degree of closeness between the sample data and the parametric model as a function of an unknown parameter; the degree of closeness is described by some notion of affinity, or inversely, by some notion of distance, between the data and the model. Thus, for example, the estimate of the unknown parameter will be obtained by minimizing a suitable distance over the parameter
1st Edtion
13: 978-1-4200-9966-
NONE
Statistical Inference
Management
English
Taylor & Francis Group, LLC
2011
USA
1-424
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