Definition
Let be an independent and identically distributed (iid) random sample from a population with distribution and .
Let be the empirical distribution function based on the sample.
Let be an estimator for . Then is an estimator for .
Let be a functional returning some measure of "distance" between the two arguments. The functional is also called the criterion function.
If there exists a such that, then is called the minimum distance estimate of .
(Drossos & Philippou 1980, p. 121)
Read more about this topic: Minimum Distance Estimation
Famous quotes containing the word definition:
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)