Efficient Uk's Re-descending M-estimator for Robust Regression.

Umair Khalil; Amjad Ali; Dost Muhammad Khan; Sajjad Ahmad Khan; Fazli Qadir; Alamgir

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Efficient Uk's Re-descending M-estimator for Robust Regression.

Author(s)

Umair Khalil Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan

Amjad Ali Department of Statistics, Islamia College Peshawar, Pakistan

Dost Muhammad Khan Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan

Sajjad Ahmad Khan Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan

Fazli Qadir Department of Statistics, University of Peshawar, Peshawar, Pakistan

Alamgir Department of Statistics, University of Peshawar, Peshawar, Pakistan

Abstract

M-estimators are used as a robust replacement of the general classical estimators used in the field of statistics. Redescending M-estimators are those estimators which rejects the extreme values completely. We developed a new redescending M-estimator “Uk's redescending M-estimator” for robust regression and detection of outlier, which will provide protection against outliers. Moreover the y -function of the Uk's estimator is more linear in the central segment before it redescends. Simulation studies shows that Uk's Redescending M-estimator is more efficient than the other estimators. We also have applied the estimator to the real world data taken from the literature. The newly developed Uk's Redescending M-estimator give a general idea to interconnect all the Redescending M-estimators with that of the idea used in Andrews sine function. A couple of which has been solved and the rest are under study for the mathematical solution. Another purpose of the present work is to develop a robust estimator. Like OLS estimator the formula for the estimation of standard errors is not available for robust estimators which is required for inferences purposes. So, here as an additional work, we have tried to find out standard errors of these estimators by using bootstrap method.

Publication Details

Page(s) 125-138

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 32, Issue: 2, Year: 2016

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