Least squares estimation of a quasiconvex regression function
提出一种基于拟凸性和单调性经济公理的多变量函数估计新方法，通过混合整数二次规划计算约束最小二乘估计量，并给出有限样本风险界，模拟和实证（日本胶合板行业生产函数、美国医院成本函数）显示其优于竞争方法。
Abstract 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 characterisation 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.