Bootstrap Methods for Median Regression Models
针对中位数回归的最小绝对离差估计量目标函数不光滑的问题，本文通过平滑目标函数得到渐近等价的估计量，并证明基于该估计量的对称t和卡方检验在Bootstrap临界值下具有更优的渐近精度，适用于删失中位数回归模型。
The least-absolute-deviations (LAD) estimator for a median-regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective function. The smoothed estimator is asymptotically equivalent to the standard LAD estimator. With bootstrap critical values, the rejection probabilities of symmetrical t and X 2 tests based on the smoothed estimator are correct through O(n -γ ) under the null hypothesis, where γ<1 but can be arbitrarily close to 1. In contrast, first-order asymptotic approximations make errors of size O(n -γ ). These results also hold for symmetrical t and X 2 tests for censored median regression models.