发表机构
University of Bonn（波恩大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究线性不等式约束下投影几何的选择，提出在二次损失下最小化最坏边界风险并满足局部无损害条件的方法，以改善估计风险。
AI 中文摘要
经济理论经常对感兴趣的参数或函数施加线性不等式约束。施加此类约束的一种常见方法是将无约束估计量投影到可行集上。投影估计量自然产生于约束最小二乘、工具变量、广义矩方法、最大似然及相关极值程序。当抽样协方差、损失函数和投影准则导致不同的几何形状时，投影几何的选择会显著影响风险。我们在二次损失下，于固定维数的局部高斯实验中研究这一选择。在只有一条维持的不等式起作用的精确边界配置下，逆协方差投影是逐点最优的。当至多两个不等式局部相关时，它在整个相应局部实验中弱优于无约束估计量，并且在精确边界配置上是极小极大的。对于任意数量的不等式，我们提供了边界极小极大性的充分条件，但通过反例表明，一旦三个不等式可以同时起作用，逆协方差投影不一定是边界极小极大的。受这些结果的启发，我们提出选择投影几何以最小化最坏情况下的边界风险，并受制于相对于无约束估计的局部无损害条件。我们开发了一种可行的实现方法，并在模拟和汽油需求的应用中研究了其有限样本性能。
英文摘要
Economic theory frequently implies linear inequality restrictions on parameters or functions of interest. A common way to impose such restrictions is to project an unrestricted estimator onto the feasible set. Projection estimators arise naturally from constrained least squares, instrumental variables, generalized method of moments, maximum likelihood, and related extremum procedures. When the sampling covariance, loss function, and projection criterion induce different geometries, the choice of projection geometry can substantially affect risk. We study this choice in a fixed-dimensional local Gaussian experiment under quadratic loss. At exact-boundary configurations where only one maintained inequality binds, inverse-covariance projection is pointwise optimal. When at most two inequalities are locally relevant, it weakly improves on the unrestricted estimator throughout the corresponding local experiment and is minimax over exact-boundary configurations. For an arbitrary number of inequalities, we provide a sufficient condition for boundary minimaxity, but show by counterexample that inverse-covariance projection need not be boundary minimax once three inequalities can bind. Motivated by these results, we propose selecting the projection geometry to minimize worst-case boundary risk subject to a local no-harm condition relative to unrestricted estimation. We develop a feasible implementation and study its finite-sample performance in simulations and an application to gasoline demand.
