Open Access

ARTICLE

Generalized Class of Mean Estimators with Known Measures for Outliers Treatment

Ibrahim M. Almanjahie^1,2, Amer Ibrahim Al-Omari^3,*, Emmanuel J. Ekpenyong⁴, Mir Subzar⁵

1 Department of Mathematics, College of Science, King Khalid University, Abha, 62529, Saudi Arabia
2 Statistical Research and Studies Support Unit, King Khalid University, Abha, 62529, Saudi Arabia
3 Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, 25113, Jordan
4 Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia, Nigeria
5 Jammu and Kashmir Institute of Mathematical Sciences, Srinagar, 190008, India

* Corresponding Author: Amer Ibrahim Al-Omari. Email:

Computer Systems Science and Engineering 2021, 38(1), 1-15. https://doi.org/10.32604/csse.2021.015933

Received 14 December 2020; Accepted 14 January 2021; Issue published 01 April 2021

Abstract

In estimation theory, the researchers have put their efforts to develop some estimators of population mean which may give more precise results when adopting ordinary least squares (OLS) method or robust regression techniques for estimating regression coefficients. But when the correlation is negative and the outliers are presented, the results can be distorted and the OLS-type estimators may give misleading estimates or highly biased estimates. Hence, this paper mainly focuses on such issues through the use of non-conventional measures of dispersion and a robust estimation method. Precisely, we have proposed generalized estimators by using the ancillary information of non-conventional measures of dispersion (Gini’s mean difference, Downton’s method and probability-weighted moment) using ordinary least squares and then finally adopting the Huber M-estimation technique on the suggested estimators. The proposed estimators are investigated in the presence of outliers in both situations of negative and positive correlation between study and auxiliary variables. Theoretical comparisons and real data application are provided to show the strength of the proposed generalized estimators. It is found that the proposed generalized Huber-M-type estimators are more efficient than the suggested generalized estimators under the OLS estimation method considered in this study. The new proposed estimators will be useful in the future for data analysis and making decisions.

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Citations