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.

Keywords

Main Subjects

References

4XDQWLOH UHJUHVVLRQ PRGHO DQG LWV JHQHUDOL]DWLRQV LQFOXGLQJ 0TXDQWLOH UHJUHVVLRQPRGHODUHDQDO\]HGXVXDOO\YLDDQRQSDUDPHWULFDSSURDFKDQGWKHLU SDUDPHWHUV DUH HVWLPDWHG XVLQJ VRPHLWHUDWLYH RSWLPL]DWLRQ DOJRULWKPV
WKHVHUHDVRQLQWKHVHPRGHOVFRQILGHQFHLQWHUYDOVDQGK\SRWKHVHVWHVWLQJKDYH GRQHSHUIRUFHXVLQJUDQNEDVHGRUERRWVWUDSSLQJDSSURDFKHV,QWKLVSDSHUZH FRQVLGHU SDUDPHWULF DQDO\VLV RI 0TXDQWLOH PRGHO ,W LV VKRZQ WKDW
WKH IUHTXHQWLVWEDVHGDSSURDFKRIPD[LPXPOLNHOLKRRGHVWLPDWLRQOHDGVWRUHVXOWV WKDWDUHVLPLODUWRWKHQRQSDUDPHWULFDSSURDFK+HQFHLQRUGHUWRDFKLHYHD PRUHDIILFLHQWPRGHOZHKDYHEHHQXVHGWKH%D\HVWKHRU\DQGDKLHUDUFKLFDO %D\HVPRGHOKDVEHHQGHYHORSHG7KHHIILFLHQF\RIWKHSURSRVHGPRGHOKDV EHHQDVVHVVHGYLDDVLPXODWLRQVWXG\DQGUHDOZRUGH[DPSOH
KHUHVXOWVVKRZ WKDWWKH%D\HVLDQDSSURDFKRIPTXDQWLOHUHJUHVVLRQDQDO\VLVLVPRUHHIILFLHQW WKDQWKHFRUUHVSRQGIUHTXDQWLVWDSSURDFKIRUDOOVDPSOHVL]HV,QDGGLWLRQWKH SURSRVHG PRGHO WUXO\ WDNHV LQWR DFFRXQW WKH HIIHFW RI WKH RXWOLHU REVHUYDWLRQ ZKLFK FDXVHV VNHZQHVV LQ UHVSRQVH YDULDEOH GLVWULEXWLRQ LQ PRGHOLQJ
Journal of Advanced Mathematical Modeling
Volume 7, Issue 2
April 2018
Pages 61-84

Files

History

  • Receive Date: 21 August 2016
  • Revise Date: 30 March 2018
  • Accept Date: 17 February 2018

Share

How to cite

Statistics