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Title:	Classical and bayesian inference for linear regression models under alpha skew normal and extended skew normal distributions
Authors:	Ali Ahmed Abdullah Alhamed (P65908)
Supervisor:	Kamarulzaman Ibrahim, Prof.Dr.
Keywords:	Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia Bayesian statistical decision theory Distribution (Probability theory) Skew fields
Issue Date:	17-Apr-2017
Description:	Various interesting applications of linear regression models involve the assumption that the error term is normally distributed. However, due to certain reasons, the assumption of normality is often not fulfilled. This could be due to the presence of high skewness and fat tails in the data. Since the data exhibit the property of being highly skewed, some authors have assumed replacing the normality assumption with certain class of asymmetrical distributions such as the skew normal distributions. Although, there are some studies which have considered regression modelling involving the skew normal error, there are not much works which consider the random error as following the extended skew normal distribution, which is a generalization of the skew normal distribution. Accordingly, we extend the idea in the linear regression model under normal error by assuming that the error term follows the extended skew normal distribution. This assumption allows for a greater flexibility when accommodating skewness in the data. Under the assumption that the error term follows the extended skew normal distribution the regression parameters are estimated based on the maximum likelihood and least squares methods. The asymptotic distribution of the maximum likelihood estimators are also studied. Based on some simulation study, it is found that the estimators are more precise under extended skew normal errors as compared to the normal errors. In addition, the estimators for both cases when the errors are assumed to follow the normal and the extended skew normal distributions are also estimated and compared under the Bayesian approach. In the Bayesian methods, certain hierarchical representations of the parameters are adopted. We found that the Bayes estimators under the extended skew normal error are more precise than the corresponding estimators under the normal error. Moreover, in the Bayesian linear regression model under the normal error, we consider the alpha skew normal priors. Based on the credible intervals and posterior predictive intervals, the performance of the Bayes estimators under alpha skew normal prior are compared to the corresponding Bayes estimators when the normal prior and non-informative prior are assumed. It is found that the Bayes estimators are more precise under alpha skew normal prior as opposed to the normal prior. We further provide the derivation of Bayes factor for the purpose of hypothesis testing in the case of Bayesian linear regression model under extended skew normal error and alpha skew normal prior, and in addition we also investigate the posterior predictive distribution. Finally, the application of the classical and Bayesian models which have been introduced are demonstrated using some real data.,Certification of Masters/ Doctorial Thesis" is not available
Pages:	160
Call Number:	QA279.5.A437 2017 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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