GLS under monotone heteroskedasticity
提出一种在非参数单调性约束下估计条件方差函数的方法，利用等渗回归实现广义最小二乘估计，无需参数形式或平滑参数，且渐近等价于已知方差时的理想估计。
The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive functional form assumption for parametric estimation or smoothing parameters for nonparametric estimation. In this paper, we propose an alternative approach to estimate the conditional variance function under nonparametric monotonicity constraints by utilizing the isotonic regression method. Our GLS estimator is shown to be asymptotically equivalent to the infeasible GLS estimator with knowledge of the conditional error variance, and involves only some tuning to trim boundary observations, not only for point estimation but also for interval estimation or hypothesis testing. Simulation studies and an empirical example illustrate excellent finite sample performances of the proposed method.