Journal of Advances in Applied Mathematics

Download PDF (748.8 KB) PP. 197 - 207 Pub. Date: October 24, 2017

DOI: 10.22606/jaam.2017.24001

• Abdulhussein Saber AL-Mouel
  Mathematics Department College of Education for Pure Sciences, AL-Basrah University, Iraq
• Ameera Jaber Mohaisen^*
  
  Mathematics Department College of Education for Pure Sciences, AL-Basrah University, Iraq

In this paper, Bayesian approach based on Markov chain Monte Carlo (MCMC) to (fully) Semiparametric regression problems is described as a mixed model using a convenient connection between penalized splines and mixed models. We investigate the inferences on the model coefficients under some conditions on the prior, as well as studying some properties of the posterior distribution and identifying the analytic form of the Bayes factors.

Semiparametric regression, penalized spline, mixed model, bayes approach, prior distribution, posterior distribution, bayes factor.

[1] Brezger, Andereas, Kneib, Thomas and Lang, Stefan, "Analyzing Bayesian semiparametric regression models", Work shop AG-Bayes, Universitat München, 2002.

[2] Choi, T., Lee, J. and Roy, A., "A note on the Bayes Factor in a Semiparametric regression model", Journal of Multivariate Analysis, 316-1327, 2008.

[3] Jensen, M. J. and Maheu, J. M.,"Bayesian Semiparametric stochastic volatility modeling”, The Rimini Center for Economic Analysis, Italy, 2007.

[4] Jonsson, R. A. and Wichern, D. W. "Applied Multivariate Statistical Analysis" Prentice Hall, Englewood Cliffs, New Jersey 07632, 1988.

[5] Jon, W., "Bayesian and frequentist regression methods, Springer New York Heidelberg Dordrecht London, (2013).

[6] Lenk, P. J., "Bayesian inference for Semiparametric regression using a Fourier representation ", J.R. Statist. Soc. Ser. B61, part 4, 1999.

[7] Mohaisen, A. J. and Abdulhussain, A. M., "A note on Bayes Semiparametric regression ", Mathematical Theory and Modeling www.iiste.org ISSN (Paper)2224-5804 ISSN (Online)2225-0522 Vol.3, No. 12, 2013.

[8] Mohaisen, A. J. and Abdulhussain, A. M., "Bayesian Semiparametric regression with fuzzy sets ", International Journal of Pure and Applied Research in Engineering and Technology IJPRET, Vol. 2 (3):1-18 IJPRET, Research article ISSN: 2319-507X, 2013.

[9] Mohaisen, A. J. and Abdulhussain, A. M., "Fuzzy sets and penalized spline in Bayesian Semiparametric regression ", LAP LAMBERT Academic Publishing, ISBN: 978-3-659-18439-0, 2014.

[10] Natio, K., "Semiparametric regression with multiplicative adjustment, communications in statistics, theory and methods", 31 2289-2309, 2002.

[11] Pelenis, J., "Bayesian Semiparametric Regression" Institute for Advanced Studies, Vienna 1-39, (2012).

[12] Ruppert, D., Wand, M.P. and Carroll, R. J. "Semiparametric regression", Cambridge university press, (2003).

[13] Temaratram, K., Robust estimation and model selection in Semiparametric regression models", Proefschrift voorgedragen tot het behalen van de grad van Doctor in de Toegepaste Economische Wetenschappen door, (2011).

[14] Tsiatis, A. A. and MA, Y., "locally efficient Semiparametric estimators for functional measurement error models ", Biometrika, 91, 4, pp.835-848, 2004.

[15] Wand, M.P. "Semiparametric regression and graphical models". Aust, N. Z. J. Stat., 51 (1), 2009.

[16] Yuan, A. and DE Gooijer, J.G. "Semiparametric regression with kernel error model", Board of the Foundation of the Scandinavian Journal of statistics, Published by Blackwell Publishing Ltd, 2007.