Censored Discrete Linear $l_1 $ Approximation
Censored Discrete Linear $l_1 $ Approximation
复制标题
截尾离散线性 $l_1 $ 近似
DOI：
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
R. Womersley
中科院分区：
文献类型：
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作者：
R. Womersley
截尾线性l_1逼近问题是使非凸分段线性函数F（x）= sum _{i = 1}^m最小化|y_i - max（z_i，x^T a_i）|$.这个问题出现在因变量范围受限的回归模型中。与极大似然估计和最小二乘估计不同，截尾估计不需要假设误差服从正态分布就能提供相容估计，本文给出了F的广义梯度的一个紧刻画，以及F的（严格）局部极小的充要条件。本文推广了线性规划的既约梯度算法和L1逼近，给出了一个稳定的有限直接下降法，用于计算F的局部极小值。这提供了一种计算截尾l_1估计量的有效方法。
The censored linear $l_1 $ approximation problem is to minimize the nonconvex piecewise linear function $F(x) = sum _{i = 1}^m |y_i - max (z_i ,x^T a_i )|$. The problem arises in regression models where the range of the dependent variable is restricted. Unlike the maximum likelihood and least squares estimators the censored $l_1 $ estimator provides a consistent estimator without an assumption that the errors are normally distributed.This paper presents a compact characterization of the generalized gradient of F, and necessary and sufficient conditions for a (strict) local minimizes of F. A reduced gradient algorithm for linear programming and $l_1 $ approximation is extended to provide a stable finite direct descent method, for calculating a local minimizes of F. This provides an efficient method of calculating the censored $l_1 $ estimator.