Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,14
We consider chi-squared type tests for testing the hypothesis H 0 that a density f of observations X1,..., Xn lies in a parametric class of densities F. We consider a version of chi-squared type test using kernel estimates for the density. The main result is, following Liero, Läuter and Konakov (1998) the derivation of the asymptotic behavior of the power of the test under Pitman and sharp peak type alternatives. The connection of the rate of convergence of these local alternatives, the bandwidth of the kernel estimator, the parametric estimator, the power of the test are studied.
maximum likelihood estimator local alternative asymptotic power Chi-squared test Goodness-of-fit test Density kernel estimators Pitman alternative sharp peak alternative