Efficient Estimation for Models With Nonlinear Heteroscedasticity
针对非线性异方差模型的两步分位数回归中初步估计量带来的问题，提出一种跨分位数加权约束估计方法，在最优权重下消除初步估计影响并接近Cramér-Rao下界，蒙特卡洛和GDP通胀率应用显示效率提升。
We study efficient estimation for models with nonlinear heteroscedasticity. In two-step quantile regression for heteroscedastic models, motivated by several undesirable issues caused by the preliminary estimator, we propose an efficient estimator by constrainedly weighting information across quantiles. When the weights are optimally chosen under certain constraints, the new estimator can simultaneously eliminate the effect of preliminary estimator as well as achieve good estimation efficiency. When compared to the Cramér-Rao lower bound, the relative efficiency loss of the new estimator has a conservative upper bound, regardless of the model design structure. The upper bound is close to zero for practical situations. In particular, the new estimator can asymptotically achieve the optimal Cramér-Rao lower bound if the noise has either a symmetric density or the asymmetric Laplace density. Monte Carlo studies show that the proposed method has substantial efficiency gain over existing ones. In an empirical application to GDP and inflation rate modeling, the proposed method has better prediction performance than existing methods.