Nonparametric goodness-of-fit tests when checking composite hypotheses
B. Yu. Lemeshko, Sergey N. Postovalov · Proceedings Third Russian-Korean International Symposium on Science and Technology. KORUS'99 (Cat. No.99EX362) · 2005
Using methods of computer simulation it has been s hown that when checking composite hypotheses the distributions of statistic s of nonparametric goodness-of-fit tests depend not only on the law F x ( , ) θ , corresponding to hypothesis H 0 , but also on the method of estimating the parameter θ . It has been shown that tests have a maximum power when using maximum likelihood method. With usage of goodness-of-fit tests the simple hypo theses of the form H 0 : F x F x ( ) ( , ) = θ , where F x ( , ) θ - the cumulative distribution function, with which is checked goodness-of-fit of observed sample, θ - known value of the parameter (scalar or vectoria l), and composite hypotheses H0 : F x F x ( ) ( , ɵ )