Estimating Box-Cox power transformation parameter via goodness-of-fit tests

Goodness-of-fit Tests via Phi-divergences

By Leah Jager∗ and Jon A. Wellner† Grinnell College and University of Washington A unified family of goodness-of-fit tests based on φ−divergences is introduced and studied. The new family of test statistics Sn(s) includes both the supremum version of the Anderson-Darling statistic and the test statistic of Berk and Jones (1979) as special cases (s = 2 and s = 1 respectively). We also introduce ...

Power Comparison of Some Goodness-of-fit Tests

Global Power Functions of Goodness of Fit Tests

It is shown that the global power function of any nonparametric test is flat on balls of alternatives except for alternatives coming from a finite dimensional subspace. The present benchmark is here the upper one-sided (or two-sided) envelope power function. Every choice of a test fixes a priori a finite dimensional region with high power. It turns out that also the level points are far away fr...

Improved Power in Multinomial Goodness-of-fit Tests

The Pearson’s chi-square and the log likelihood ratio chi-square statistics are fundamental tools in goodnessof-fit testing. Cressie and Read (1984) constructed a general family of divergences which includes both statistics as special cases. This family is indexed by a single parameter, and divergences at either end of the scale are more powerful against alternatives of one type while being rat...

The Comparison Between Goodness of Fit Tests for Copula

‎Copula functions as a model can show the relationship between variables‎. ‎Appropriate copula function for a specific application is a function that shows the dependency between data in a best way‎. ‎Goodness of fit tests theoretically are the best way in selection of copula function‎. ‎Different ways of goodness of fit for copula exist‎. ‎In this paper we will examine the goodness of fit test...