AN EFFICIENT AND HIGH BREAKDOWN ESTIMATION PROCEDURE FOR NONLINEAR REGRESSION MODELS

Dost Muhammad Khan; Shumaila Ihtesham; Amjad Ali; Umair Khalil; Alamgir; Sajjad Ahmad Khan; Sadaf Manzoor

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AN EFFICIENT AND HIGH BREAKDOWN ESTIMATION PROCEDURE FOR NONLINEAR REGRESSION MODELS

Author(s)

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

Shumaila Ihtesham Department of Statistics, Islamia College Peshawar,KP,Pakistan

Amjad Ali Department of Statistics, Islamia College Peshawar,KP,Pakistan

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

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

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

Sadaf Manzoor Department of Statistics, Islamia College Peshawar,KP,Pakistan

Abstract

In regression analysis least square (LS) estimator fails because of its sensitivity to unusual observations present in the data. Robust estimation provides alternative estimates which are insensitive and efficient, when the data are not normally distributed or polluted with distant observations usually called outliers. To cope with the problem of outliers is more challenging in nonlinear regression (NLRM) than linear regression. In this study, least trimmed absolute (LTA) estimator which is a robust and high breakdown estimator is adopted for nonlinear regression model fitting. Bias and mean square error is used to check the efficiency of the proposed estimator. The performance of the estimator is compared with LS and existing robust M-estimators using simulated data sets and real world problems. It has been observed that LTA is efficient in case of contaminated data sets as compared to LS and M estimator. Furthermore, it has been concluded that in case of 40% contamination LTA outperforms LS and M estimator, while in case of 20% outliers LTA and M estimators perform equally well. In regard to clean data sets, LS, LTA and M estimator performs equally well. Conclusion has been made on the basis of simulated data sets as well as real data sets.

Publication Details

Page(s) 223-236

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 33, Issue: 3, Year: 2017

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Keywords

M-estimator, High Breakdown, outliers, nonlinear least squares, leverage points, least trimmed square

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