A Bayesian Approach to Quantile Regression for Interval-Valued Data: Application to CAPM

Abstract

The purpose of this paper is to introduce an approach to fitting a quantile regression on interval-valued data. This approach consists of fitting a model on the appropriate point of the interval values. To obtain this point, the convex combination method is applied in the quantile regression. Moreover, we also introduce the Bayesian approach for estimating all the unknown parameters in the model. The approach is illustrated via a simulation study and real data sets. In the real data study, we apply this methodology to measure the beta risk of Thai stock returns through Capital Asset Pricing model. The results show the high performance and accuracy of the Bayesian estimation in both simulated data and real application study.