Hierarchical Bayes M-Quantile Regression Analysis Under Type 2 Huber Loss

Document Type : Original Paper

Authors

Department of Statistics, Imam Khomeini International University, Ghazvin, Iran

Abstract

‎Quantile regression model and its generalizations‎, ‎including M-quantile regression model‎, ‎are analyzed usually via a nonparametric approach and their parameters are estimated using some iterative optimization algorithms‎. ‎For these reason‎, ‎in these models confidence intervals and hypotheses testing have done perforce using rank-based or bootstrapping approaches‎. ‎In this paper‎, ‎we consider parametric analysis of M-quantile model‎. ‎It is shown that‎, ‎the frequentist based approach of maximum likelihood estimation leads to results that are similar to the nonparametric approach‎. ‎Hence‎, ‎in order to achieve a more afficient model‎, ‎we have been used the Bayes theory and a‎ ‎hierarchical Bayes model has been developed‎. ‎The efficiency of the proposed model has been assessed via a simulation study and real word example‎. The ‎results ‎show ‎that ‎the ‎Bayesian ‎approach of ‎m-quantile ‎regression ‎analysis ‎is ‎more ‎efficient ‎than ‎the correspond ‎frequantist ‎appro‎ach, for all sample sizes. In addition, the proposed model truly takes into account the effect of the outlier observation, which causes skewness in response variable distribution, in modeling.

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