On Computer-Intensive Estimation and Testing Procedures in Econometrics

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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.