Cramér-von Mises statistics based on the sample quantile function and estimated parameters
The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in \(L^ 2(0,1)\) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for testing a composite null hypothesis based on the sample quantile function and estimated parameters. Special emphasis is given to the location/scale composite null hypothesis.
estimated weighted empirical quantile process
asymptotic null distribution of Cramér-von Mises type statistics
scientific article; zbMATH DE number 3934200
scientific article