Research in Econometric Methods

该提案描述了几个新课题的研究和几个领域的持续研究。首先，PI将考虑长内存参数‘d’的偏置减少半参数估计。这个参数最常见的估计量，Geweke和Porter-Hudak （GPH）估计量，已经被发现有很大的有限样本偏差。PI和耶鲁大学的研究生P. Guggenberger将开发一种替代GPH估计器，其偏差减少了一个数量级，其方差仅通过乘法常数增加，其收敛速度比GPH估计器更快。我们计划建立当归一化谱密度在零处平滑为s阶时，‘d’估计器的最优收敛率，并表明减少偏置的GPH估计器达到了这个速率，但是，对于s 2， GPH估计器没有。PI将与耶鲁大学的研究生孙逸潇合作，开发一个局部多项式惠特尔估计器，它的行为与其他局部惠特尔估计器相似，但偏差减少，收敛速度更快。提出研究的第二个领域是非线性估计器的自举。这项研究继续了PI已经报道的工作。我们的目标是获得自举最小距离和间接推理估计器的高阶改进，iid非参数自举的高阶改进结果比现有的结果更强，以及基于残差和BCa自举以及拉格朗日乘子（LM）和似然比（LR）检验的新结果。第三个研究领域是开发经典LM、LR和Wald检验的一些新的渐近最优性性质。我们的想法是推广这一发现，即针对AR(1)误差的序列相关性的LM测试与针对MA(1)误差的LM测试相同。这一发现意味着LM、LR和Wald检验对AR(1)和MA(1)误差的检验都具有Wald型渐近最优性。这种类型的结果更普遍地适用于本模型和许多其他模型。提出研究的目的是获得一些一般结果，以确定给定LM， LR或Wald检验具有渐近最优性的不同类别的备选模型。提议研究的第四个领域继续PI的研究，即当参数在维持假设的边界上并且参数出现在替代假设下而不是在零假设下时的测试问题。这类问题的例子已经很多了，我们相信随着研究人员越来越多地依赖非线性模型，这类问题将变得越来越普遍。我们的目标是证明LR、LM和Wald检验是渐近允许的，开发新的检验，使某些权函数的加权平均幂最大化，构造一个完整的检验类，并建立Markov状态切换模型中LR、LM和Wald检验的渐近零分布。最后，我们计划证明用于检验GARCH（1,1）形式的条件异方差的LR、LM和Wald检验在平方误差中对任何形式的序列相关都是一致的。

This proposal describes research on several new topics and continued research in several areas. First, the PI will consider bias-reduced semiparametric estimation of the long memory parameter 'd'. The most common estimator of this parameter, the Geweke and Porter-Hudak (GPH) estimator, has been found to have substantial finite sample bias. The PI and P. Guggenberger, a graduate student at Yale, will develop an alternative GPH estimator whose bias is reduced by an order of magnitude, whose variance is increased only by a multiplicative constant, and whose rate of convergence is faster than that of the GPH estimator. We plan to establish the optimal rate of convergence of estimators of 'd' when the normalized spectral density is smooth of order s at zero and show that the bias-reduced GPH estimator attains this rate, but, for s 2, the GPH estimator does not. Working with Yixiao Sun, a graduate student at Yale, the PI will develop a local polynomial Whittle estimator that behaves like other local Whittle estimators, but has reduced bias and a faster rate of convergence.The second area of proposed research is on the bootstrap for nonlinear estimators. This research continues work already reported by the PI.. We aim to obtain higher-order improvements for bootstrapping minimum distance and indirect inference estimators, stronger higher-order improvement results for the iid nonparametric bootstrap than those currently available, and new results for residual-based and BCa bootstraps and Lagrange multiplier (LM) and likelihood ratio (LR) tests.The third area of research is to develop some new asymptotic optimality properties of the classical LM, LR, and Wald tests. The idea is to generalize the finding that the LM test for serial correlation against AR(1) errors is the same as that against MA(1) errors. This finding implies that the LM, LR, and Wald tests have Wald-type asymptotic optimality properties for testing against both AR(1) and MA(1) errors. Results of this type hold more generally, both in this model and in many other models. The object of the proposed research is to obtain some general results that determine different classes of alternative models for which a given LM, LR, or Wald test has asymptotic optimality properties.The fourth area of proposed research continues the PI's research on testing problems when a parameter is on the boundary of the maintained hypothesis and a parameter appears under the alternative but not under the null hypothesis. Numerous examples of such problems already exist, and we believe that problems of this sort will become increasingly prevalent as researchers rely more and more on nonlinear models. We aim to show that the LR, LM, and Wald tests are asymptotically admissible, develop new tests that maximize weighted average power for certain weight functions, construct a complete class of tests, and establish the asymptotic null distribution of the LR, LM, and Wald tests in the Markov regime switching model. Finally, we plan to show that the LR, LM, and Wald tests for testing for conditional heteroskedasticity of GARCH(1, 1) form are consistent against any form of serial correlation in the squared errors.