Efficient Estimation for Models With Nonlinear Heteroscedasticity

We study efficient estimation for models with nonlinear heteroscedasticity. In two-step quantile regression heteroscedastic models, motivated by several undesirable issues caused the preliminary estimator, we propose an estimator constrainedly weighting information across quantiles. When weights are optimally chosen under certain constraints, new can simultaneously eliminate effect of as well achieve good efficiency. compared to Cramér-Rao lower bound, relative efficiency loss has a conservative upper regardless model design structure. The bound is close zero practical situations. particular, asymptotically optimal if noise either symmetric density or asymmetric Laplace density. Monte Carlo studies show that proposed method substantial gain over existing ones. empirical application GDP and inflation rate modeling, better prediction performance than methods.