Components of Goodness-of-Fit Statistics.
Abstract
In a recent paper, Durbin and Knott (DK) (1972) partitioned the Cramer-von Mises statistic W sup 2, used for tests of goodness-of-fit, into an infinite set of components. For the case when the hypothesised distribution function is completely specified, these components have the interesting property that they all have the same distribution, to within a constant. Durbin and Knott suggested the use of some of the components as test statistics, and investigated their asymptotic powers, compared with W sup 2, for the case when the distribution tested on Ho is N(0,1), and when the family of alternatives has a different mean or a different variance. The purpose of this paper is to provide various extensions of the DK results with the intention of further illuminating the properties of the components and the entire statistics, particularly with respect to power.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 22, 1974
- Accession Number
- ADA013277
Entities
People
- M. A. Stephens
Organizations
- Stanford University