Parametric Bootstrap Methods for Parameter Estimation in SLR Models

Abstract

The purpose of this study is to investigate the performance of the bootstrap method on external sector statistics (ESS) in the Nigerian economy. It was carried out using the parametric methods and comparing them with a parametric bootstrap method in regression analysis. To achieve this, three general methods of parameter estimation: least-squares estimation (LSE) maximum likelihood estimation (MLE) and method of moments (MOM) were used in terms of their betas and standard errors. Secondary quarterly data collected from Central Bank of Nigeria statistical bulletin 2012 from 1983-2012 was analyzed using by S-PLUS softwares. Datasets on external sector statistics were used as the basis to define the population and the true standard errors. The sampling distribution of the ESS was found to be a Chi-square distribution and was confirmed using a bootstrap method. The stability of the test statistic was also ascertained. In addition, other parameter estimation methods like R2, R2adj, Akaike Information criterion (AIC), Schwart Bayesian Information criterion (SBIC), Hannan-Quinn Information criterion (HQIC) were used and they confirmed that when the ESS was bootstrapped it turned out to be the best model with 98.9%, 99.9%, 84.9%, 85.4% and 86.7% respectively.