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

Quantile regression model and its generalizationsý, ýincluding M-quantile regression modelý, ýare analyzed usually via a nonparametric approach and their parameters are estimated using some iterative optimization algorithmsý. ýFor these reasoný, ýin these models confidence intervals and hypotheses testing have done perforce using rank-based or bootstrapping approachesý. ýIn this paperý, ýwe consider parametric analysis of M-quantile modelý. ýIt is shown thatý, ýthe frequentist based approach of maximum likelihood estimation leads to results that are similar to the nonparametric approachý. ýHenceý, ýin order to achieve a more afficient modelý, ýwe have been used the Bayes theory and aý ýhierarchical Bayes model has been developedý. ýThe efficiency of the proposed model has been assessed via a simulation study and real word exampleý. The ýresults ýshow ýthat ýthe ýBayesian ýapproach of ým-quantile ýregression ýanalysis ýis ýmore ýefficient ýthan ýthe correspond ýfrequantist ýapproýach, 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.