Statistical inference the minimum distance approach - Basu, Ayanendranath; Shioya, Hiroyuki; Park, Chanseok (Monographs on statistics and applied probability, 2011)
"Preface In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. A parametric model imposes a certain structure on the class of probability distributions that may be used to describe real life data generated from a process under study. There hardly appears to be a better way to deal with such a problem than to choose the parametric model that minimizes an appropriately defined distance between the data and the model. The issue is an important and complex one. There are many different ways of constructing an appropriate "distance" between the "data" and the "model". One could, for example, construct a distance between the empirical distribution function and the model distribution function by a suitable measure of distance. Alternatively, one could minimize the distance between the estimated data density (obtained, if necessary, by using a nonparametric smoothing technique such as kernel density estimation) and the parametric model density. And when the particular nature of the distances have been settled (based on distribution functions, based on densities, etc.), there may be innumerable options for the distance to be used within the particular type of distances. So the scope of study referred to by "Minimum Distance Estimation" is literally huge"--Provided by publisher