Bayesian Binary Quantile Regression restricted by reciprocal penalty functions (with practical application)

A thesis

submitted to the council of the College of Administration and Economics at the University of Karbala as partial fulfillment of the requirements for the degree Doctorate of Philosophy in Statistics

By

Mohammed Taleb kahnger

Under Supervision

Prof. Dr. Ahmad Naeem Flaih

Quantile regression is one of the methods that has taken a wide space in application in the previous two decades because of the attractive features of these methods to researchers, as it is not affected by outliers  values, meaning that it is considered one of the robust  methods, and it gives more details of the effect of explanatory variables on the dependent variable.

There are many researchers who have addressed the issue of quantile regression with binary data, that is, when the response variable (y) takes only two values, either (0) or (1) using classical methods and also  Bayesian methods. In this study, the researcher is trying to build a model for analyzing binary data using the quantile regression method (QR), as the Bayesian method was adopted, and it is one of the methods that has received wide resonance in recent times because of its accuracy, especially in small samples.

In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantitative regression is proposed. Current approaches to variable selection in the context of binary classification are sensitive to outliers, heteroskedasticity values, or other anomalies. The proposed method in this study overcomes these problems in an attractive and straightforward way.

In addition, the researcher restricted the study by using inverse penalty functions to choose the explanatory variables that have an effect on the truly dependent variable and to exclude the unaffected variables using the methods of selecting variables.

And using the effective (Gibbs Sampler) algorithm to estimate the parameters of the model that outperforms on the (Metropolis) algorithm used in previous studies. The results of both the simulation study and the analysis of real data showed that the proposed method (BrLBqr) outperforms in terms of estimating the parameters of the model and selecting explanatory variables related to or affecting the response variable compared to the other methods (BLBqr) and (BBqr).