GENERALIZED WEIGHTED CRAMER-VON MISES DISTANCE ESTIMATORS

Generalised weighted Cramer-von Mises distance estimators in an arbitr ary model with a k-dimensional parameter vector are investigated. The distance function is defined as a function G of model-based residuals for a specified target model F and the empirical cumulative distributi on function F-n over the real line, invoking a weight function w. It i s shown that the estimator is Fisher consistent, asymptotically multiv ariate normal, and nearly efficient with desirable robustness properti es. If the true model is equal to the target model, the residual funct ion G does not affect the limiting distribution. The weight function t v controls the asymptotic distribution and the robustness of the estim ator. Three different classes of the weight functions are introduced f or different outlier patterns. These weight functions produce estimato rs asymptotically as efficient as the maximum likelihood estimators at the true model. An alternative way of calculating the estimators is c onsidered. Simulation results indicate that asymptotic results are use ful for moderate sample sizes and that the estimators are stable at th e neighbourhood of the target model.