On Computer-Intensive Estimation and Testing Procedures in Econometrics

有各种各样的非参数检验。我们考虑使用经验似然比检验检验总体均值。经验似然比检验在大样本中是有用的，但在小样本中有大小失真。对于尺寸校正，已经考虑了各种校正。在这里，我们利用Bartlett校正和自举法。本文的目的是通过蒙特卡罗实验比较$t$检验和经验似然比检验在样本功率和经验大小方面的差异。此外，我们还考虑了相关系数的非参数排列检验。由于排列检验是非常计算机密集的，所以很少有关于小样本性质的研究，尽管我们在各个方面都有很多关于渐近性质的研究。我们的目的是通过蒙特卡罗实验来比较排列检验和$t$检验，其中两个样本之间进行独立性检验。通过蒙特卡罗实验，我们得到了在底层样本非高斯分布时，非参数检验优于$t$检验的结果，并且在高斯总体下，非参数检验与$t$检验一样好。在回归模型中包含滞后因变量的情况下，已知普通最小二乘估计（OLSE）在小样本中存在偏差，并且随着不相关变量数量的增加，偏差会增加。在自举方法的基础上，尝试在自回归和非高斯情况下获得无偏估计。我们提出了基于残差的自举方法。进行了一些模拟研究，以检验所提出的估计过程是否有效。我们得到的结果是，有可能恢复真实的参数值，并且所提出的过程给出了比OLSE更小的偏估计。

There are various kinds of nonparametric tests. We consider testing population mean, using the empirical likelihood ratio test. The empirical likelihood ratio test is useful in a large sample, but it has size distortion in a small sample. For size correction, various corrections have been considered. Here, we utilize the Bartlett correction and the bootstrap method. The purpose of this paper is to compare the $t$ test and the empirical likelihood ratio tests with respect to the sample power as well as the empirical size through Monte Carlo experiments.Moreover, we consider a nonparametric permutation test on the correlation coefficient. Because the permutation test is very computer-intensive, there are few studies on small-sample properties, although we have numerous studies on asymptotic properties with regard to various aspects. We aim to compare the permutation test with the $t$ test through Monte Carlo experiments, where an independence test between two samples is taken. We obtain the results through Monte Carlo experiments that the nonparametric test performs better than the $t$ test when the underlying sample is not Gaussian and that the nonparametric test is as good as the $t$ test even under the Gaussian population.In the case where the lagged dependent variables are included in the regression model, it is known that the ordinary least squares estimates (OLSE) are biased in small sample and that the bias increases as the number of the irrelevant variables increases. Based on the bootstrap methods, an attempt is made to obtain the unbiased estimates in autoregressive and non-Gaussian cases. We propose the residual-based bootstrap method. Some simulation studies are performed to examine whether the proposed estimation procedure works well or not. We obtain the results that it is possible to recover the true parameter values and that the proposed procedure gives us the less biased estimators than OLSE.