论文标题
准方面回归函数的最小二乘估计
Least Squares Estimation of a Quasiconvex Regression Function
论文作者
论文摘要
我们开发了一种新的方法来估计基于准室内经济公理（和单调性）的多元功能。在计算方面，我们证明了准胶X限制了最小二乘估计器（LSE）的存在，并提供了通过混合整数二次二次程序来计算LSE的功能空间的表征。在理论方面，我们通过尖锐的甲骨文不等式为LSE提供有限的样本风险范围。我们的结果允许错误取决于协变量，并且只有两个有限的时刻。我们通过模拟说明了LSE与某些竞争估计器的出色性能。最后，我们使用LSE估算日本胶合板行业的生产功能以及美国整个医院的成本功能。
We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares estimator (LSE) and provide a characterization of the function space to compute the LSE via a mixed integer quadratic programme. On the theoretical side, we provide finite sample risk bounds for the LSE via a sharp oracle inequality. Our results allow for errors to depend on the covariates and to have only two finite moments. We illustrate the superior performance of the LSE against some competing estimators via simulation. Finally, we use the LSE to estimate the production function for the Japanese plywood industry and the cost function for hospitals across the US.
