Parametric Bootstrap Methods for Parameter Estimation in SLR Models

Chigozie Kelechi Acha^1,

¹Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

Cite this paper:
Chigozie Kelechi Acha. Parametric Bootstrap Methods for Parameter Estimation in SLR Models. International Journal of Econometrics and Financial Management. 2014; 2(5):175-179. doi: 10.12691/ijefm-2-5-2

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 θ was also ascertained. In addition, other parameter estimation methods like R², R²_adj, 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.

Keywords:
bootstrap parametric models parameter estimation kernel density quantile-quantile plots

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References:

[1]	Efron, B. (2000). The bootstrap and modern statistics. J. Am. Statist. Assoc. 95, 1293-1296.
[2]	Efron, B. and Tibshirani, R.J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
[3]	Freedman, D.A. (1981) Bootstrapping regression models, Ann. Statist. 6, 1218-1228.
[4]	Gonzalez-Manteiga, W. and Crujeiras, R.M. (2008). A review on goodness-of-fit tests for regression models. Pyrenees International Workshop on Statistics, Probability and Operations Research: SPO 2007, 21-59.
[5]	Good, P. (2004). Permutation, Parametric, and Bootstrap Tests of Hypotheses. 3rd Edition. Springer-Verlag, New York.
[6]	Hall, P. and Maiti, T. (2006). On parametric bootstrap methods for small area prediction. Journal of the Royal Statistical Society. Series B 68, 221-238.
[7]	Hall, P. Lee, E.R. and Park, B.U. (2009) Bootstrap-based penalty choice for the Lasso achieving oracle performance. Statistica Sinica, 19, 449-471.
[8]	Lahiri, S. N. (2006). Bootstrap Methods: A Review. In Frontiers in Statistics (J. Fan and H.L. Koul, editors) 231-265, Imperial College Press, London.
[9]	Mahiane, S. G., Nguema, E.-P. Ndong, Pretorius, C., and Auvert, B. (2010). Mathematical models for coinfection by two sexually transmitted agents: the human immunodeficiency virus and herpes simplex virus type 2 case. Appl. Statist 59, 547-572.
[10]	Papa`roditis, E. and Politis, D. (2005). Bootstrap hypothesis testing in regression models, Statistics and Probability Letters, 74: 356-365.
[11]	Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika 43: 353-360.
[12]	Xu, K. (2008). Bootstrapping autoregression under nonstationary volatility, Econometrics Journal, 11: 1-26.