Density estimation for nonlinear parametric models with conditional heteroscedasticity

摘要

This article studies density and parameter estimation problems for nonlinear parametric models with conditional heteroscedasticity. We propose a simple density estimate that is particularly useful for studying the stationary density of nonlinear timeseries models. Under a general dependence structure, we establish the root n consistency of the proposed density estimate. For parameter estimation, a Bahadur type representation is obtained for the conditional maximum likelihood estimate. The parameterestimate is shown to be asymptotically efficient in the sense that its limiting variance attains the Cramer-Rao lower bound. The performance of our density estimate is studied by simulations.