On netman-type smooth tests of fit

Abstract

. Some quadratic tests of fit related to NEYMAN'S smooth tests as well as to a class of quadratic tests of fit introduced recently by NETTHATJS (1988) are considered. Attention is focused on the case of completely specified null distribution. The case when the number of summands in the test statistics goes to infinity is discussed. In this case, asymptotic distribution under the null hypothesis as well as under some sequences of alternatives are derived by means of the KOML6S, MAJOR and TTTSNADY embedding. Using the same technique, the asymptotic distribution of the classical ehi-square test is investigated in case when the number of cells tends to infinity

Keywords:

• Test of fit
• smooth test
• quadratic statistic
• ehi-square test
• empirical process
• strong approximation
• Monte Carlo power