PAREMETRIC ANALYSIS OF M-QUANTILE REGRESSION MODELS UNDER TYPE 2 HUBER LOSS: HIERARCHICAL BAYES APPROACH

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FALLAH AFSHIN; MIRZAEE MONIR

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2018 | Volume:2 | Issue:2 Page(s): 61-84

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Title

PAREMETRIC ANALYSIS OF M-QUANTILE REGRESSION MODELS UNDER TYPE 2 HUBER LOSS: HIERARCHICAL BAYES APPROACH

Author(s)

FALLAH AFSHIN | MIRZAEE MONIR | Issue Writer Certificate

Keywords

QUANTILE REGRESSION‎Q1

‎HIERARCHICAL BAYES‎Q1

‎MAXIMUM LIKELIHOOD TYPE ESTIMATOR‎Q1

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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APA: Copy

FALLAH, AFSHIN, & MIRZAEE, MONIR. (2018). PAREMETRIC ANALYSIS OF M-QUANTILE REGRESSION MODELS UNDER TYPE 2 HUBER LOSS: HIERARCHICAL BAYES APPROACH. ADVANCES IN MATHEMATICAL MODELING, 2(2 ), 61-84. SID. https://sid.ir/paper/243864/en

Vancouver: Copy

FALLAH AFSHIN, MIRZAEE MONIR. PAREMETRIC ANALYSIS OF M-QUANTILE REGRESSION MODELS UNDER TYPE 2 HUBER LOSS: HIERARCHICAL BAYES APPROACH. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2018;2(2 ):61-84. Available from: https://sid.ir/paper/243864/en

IEEE: Copy

AFSHIN FALLAH, and MONIR MIRZAEE, “PAREMETRIC ANALYSIS OF M-QUANTILE REGRESSION MODELS UNDER TYPE 2 HUBER LOSS: HIERARCHICAL BAYES APPROACH,” ADVANCES IN MATHEMATICAL MODELING, vol. 2, no. 2 , pp. 61–84, 2018, [Online]. Available: https://sid.ir/paper/243864/en

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