Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation
研究了在误差非独立同分布的非线性动态模型中，最小绝对误差估计量的一致性和渐近正态性，并给出了协方差矩阵的一致估计量以及Wald、拉格朗日乘子和似然比检验，还提出了基于绝对残差的异方差拉格朗日乘子检验。
We consider least absolute error estimation in a dynamic nonlinear model with neither independent nor identically distributed errors. The estimator is shown to be consistent and asymptotically normal, with asymptotic covariance matrix depending on the errors through the heights of their density functions at their medians (zero). A consistent estimator of the asymptotic covariance matrix of the estimator is given, and the Wald, Lagrange multiplier, and likelihood ratio tests for linear restrictions on the parameters are discussed. A Lagrange multiplier test for heteroscedasticity based upon the absolute residuals is analyzed. This will be useful whenever the heights of the density functions are related to the dispersions.