Improved Semi-Nonparametric Estimation and Testing By Modified Likelihood

通过修正似然改进半非参数估计和检验

• 批准号: 0961596
• 负责人: Dennis Kristensen
• 金额: $ 23.58万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0961596&HistoricalAwards=false
• 关键词: Improved; Semi; Nonparametric; Estimation; Testing

Economic theory often has little to say about the specific functional forms of components entering economic models. This has lead to an increased use of non- and semiparametric estimation and testing methods in economics since these in general impose weaker functional restrictions on the models of interest.Many popular non- and semiparametric estimators involve so-called kernel-smoothing. However, these can be challenging to implement since they involve choosing appropriate bandwidths which are an integral part of the estimators: The resulting estimators are in general sensitive to the bandwidth choice. Unfortunately, theory offers few guidelines for how these should be chosen in finite samples: First of all, the bandwidth does not appear in the asymptotic distribution of the parametric estimator. Secondly, for the first-step estimation error to vanish at an optimal rate, undersmoothing is required. This rules out standard bandwidth selection methods such as plug-in and cross-validation. For a few special estimators, methods have been developed, but these can be complicated to implement and do not always perform well.We here propose a novel class of semiparametric profile estimators that do not suffer from these problems: We develop a modified version of the standard objective (likelihood) function defining the estimator. The modification entails that it can be used to estimate both the nonparametric component and the parametric one. The advantages of this modification are three-fold: First, the modification ensures that an error term normally appearing in the expansion of the parametric estimator now vanishes. Thus we expect that the modified version will have better finite-sample properties. Second, by removing the error term, we do not have to undersmooth in order for the first-step estimation error to vanish at an optimal rate. Hence standard bandwidth selection methods can be used. Finally, the proposed modified estimator is no more difficult to implement than standard estimators and require no heavy computations.We also demonstrate how the modified objective function can be used to improve on existing non- and semiparametric testing procedures using kernel-smoothing methods. The modified tests are shown to dominate the original ones in terms of Pitman's relative efficiency criterion and as such are more powerful. As with the kernel-based semiparametric estimation procedures, the issue of how to select bandwidths in the implementation of kernel-based testing procedures is to a large extent unresolved. We will examine the issue of bandwidth selection for the new class of test statistics developed in this project.The novel procedures can be used to improve upon existing econometric methods developed for many semiparametric models, including partially linear models, single-index models, (semi-)varying-coefficient models, and models with time-varying parameters. These and many other models will be considered in the project.

经济理论通常很少涉及进入经济模型的组件的具体功能形式。 这导致在经济学中越来越多地使用非参数和半参数估计和检验方法，因为这些方法通常对感兴趣的模型施加较弱的功能限制。许多流行的非参数和半参数估计涉及所谓的核平滑。 然而，这些可能是具有挑战性的实施，因为它们涉及选择适当的带宽，这是一个不可分割的一部分的估计：所得到的估计一般是敏感的带宽选择。不幸的是，理论提供了一些指导方针，这些应该如何选择在有限的样本：首先，带宽不出现在渐近分布的参数估计。 其次，为了使第一步估计误差以最佳速率消失，需要欠平滑。 这排除了标准的带宽选择方法，如插件和交叉验证。 对于一些特殊的估计，方法已经开发出来，但这些可以是复杂的实施，并不总是表现良好，我们在这里提出了一类新的半参数轮廓估计，不遭受这些问题：我们开发了一个修改后的版本的标准目标（似然）函数定义的估计。 修改后的算法既可用于估计非参数分量，也可用于估计参数分量。 这种修改的优点有三个方面：首先，修改确保了通常出现在参数估计展开式中的误差项现在消失了。 因此，我们期望修改后的版本将有更好的有限样本性质。 其次，通过去除误差项，我们不必为了使第一步估计误差以最佳速率消失而欠平滑。 因此，可以使用标准带宽选择方法。 最后，建议修改后的估计是没有更多的困难，比标准的估计，不需要繁重的computation.We还演示了如何修改后的目标函数可以用来改善现有的非和半参数测试程序，使用核平滑方法。 修改后的测试中占主导地位的原始的皮特曼的相对效率标准，因此是更强大的。与基于核的半参数估计过程一样，在基于核的测试过程的实现中如何选择带宽的问题在很大程度上是未解决的。 我们将研究在这个项目中开发的新的一类检验统计量的带宽选择的问题。新的程序可以用来改善现有的计量经济学方法开发的许多半参数模型，包括部分线性模型，单指数模型，（半）变系数模型，模型与时变参数。 这些模型和许多其他模型将在项目中加以考虑。