Smooth Bootstrap Methods on External Sector Statistics

Abstract

The investigation of the possibility of a significant difference existing in the parametric and nonparametric bootstrap methods on external sector statistics, and establishing the sample data distribution using the smooth bootstrap is the focus of this study. The root mean square error (RMSE) and the kernel density will be used on the test statistic θ in the determination of such difference. Establishing this difference will lead to more detailed study to discover reasons for such difference. This will also aid the Nigeria economy to aim at improving the performance of the external sector statistics (ESS). The study used secondary data from Central bank of Nigeria (1983-2012). Analysis was carried out using R-statistical package. In the course of the analysis, 17280 scenarios were replicated 200 times. The result shows a significant difference between the performances of the parametric and nonparametric smooth bootstrap methods, namely; wild and pairwise bootstrap respectively. The significantly better performance of the wild bootstrap indicate the possible use of this technique in assessment of comparative performance of ESS with a view to further understanding the better performers in order to identify factors contributing to such better performance. Also, when the sample size and the bootstrap level are very high, the smooth bootstrap or kernel density estimates outperform the pair wise bootstrap notwithstanding that they are nonparametric methods. The kernel density plots revealed that the sampling distribution of the ESS was found to be a Chi-square distribution and was confirmed by the smooth bootstrap methods.