Generalized R-estimators under conditional heteroscedasticity

摘要

In this paper, we extend the classical idea of Rank estimation of parameters from homoscedastic problems to heteroscedastic problems. In particular, we define a class of rank estimators of the parameters associated with the conditional mean function of an autoregressive model through a three-steps procedure and then derive their asymptotic distributions. The class of models considered includes Engel's ARCH model and the threshold heteroscedastic model. The class of estimators includes an extension ofWilcoxon-type rank estimator. The derivation of the asymptotic distributions depends on the uniform approximation of a randomly weighted empirical process by a perturbed empirical process through a very general weight-dependent partitioning argument.