Computation and Operational Properties of Nonparametric Shape-Restricted Estimators

需要参数的估计和检验方法 关于正在研究的模型中的函数的假设 重要的缺点是，当 所施加的参数限制是不正确的。 最近， 已经开发了几种估计和测试技术， 指定非参数结构，而不是指定参数结构 对模型中的功能进行限制。 典型 使用的限制是单调性，单调性和同质性。 一级，这是经济理论经常暗示的性质， 关于效用、生产、利润和成本函数的形状。 使用目前可用的算法来估计和测试 满足形状限制的非参数函数需要 更多的计算机内存和CPU时间比大多数 研究人员 该项目的主要贡献来自于 开发用于非参数估计和测试的算法， 是大多数应用研究者所能达到的。 这个项目开发了一种算法， (1)估计效用、生产、利润和成本函数， 不对这些函数施加任何参数结构，并且 (2)测试不完美的数据是否与特定的 经济假设，如最小化或最大化 假说. 更一般地说，新算法将允许 非参数形状限制函数的估计和检验 假设回归函数属于 非参数函数的特殊家族。 该算法将 与实际和模拟数据一起使用，以研究操作 非参数方法的性质，以比较 非参数方法与其参数对应物的非参数方法， 并揭示估计功能的特征， 以前使用参数方法发现的。

Estimation and testing methods that require parametric assumptions about the functions in the models being studied have the important drawback that they may yield erroneous results when the parametric restrictions imposed are incorrect. Recently, several estimation and testing techniques have been developed that, instead of specifying parametric structures, specify nonparametric restrictions about the functions in the models. Typical restrictions used are concavity, monotonicity, and homogenity of degree one, which are properties that economic theory often implies about the shape of utility, production, profit, and cost functions. Using presently available algorithms to estimate and test nonparametric functions that satisfy shape restrictions requires more computer memory and CPU time than is available to most researchers. The major contribution of this project comes from developing algorithms for nonparametric estimating and testing that are within most applied researchers' reach. This project develops an algorithm that will make it possible (1) to estimate utility, production, profit, and cost functions, without imposing any parametric structure on these functions, and (2) to test whether imperfect data are consistent with a particular economic hypothesis, such as a minimization or maximization hypothesis. More generally, the new algorithm will allow estimation of nonparametric shape-restricted functions and tests of the hypothesis that a regression function belongs to a particular family of nonparametric functions. The algorithm will be used with actual and simulated data to study the operational properties of nonparametric methods, to compare the performance of nonparametric methods with that of their parametric counterparts, and to uncover features of estimated functions that could not have been discovered previously using parametric methods.