ABSTRACT
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 consistency 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 provided useful treatments in statistical inference based on divergence measures.
