On the study of efficiency of exponential‐type estimator of population mean using robust regression methods

Abstract

This study aimed at enhancing the efficiency of Zaman estimators using exponential transformation technique. A new class of estimators was obtained using the concept of Bahl and Tuteja. The bias and mean squared error (MSE) of the new class of suggested estimators was derived up to second degree approximation. The empirical study through simulations was conducted using Normal, exponential, gamma, chi-square and beta distributions under robust regression methods (Huber-M, Huber-MM, LTS (least trimmed squares) and LMS (least median of squares)) and the results revealed that proposed estimators were more efficient. K E Y W O R D Sefficiency, exponential type estimators, robust regression, outliers INTRODUCTIONRatio, product and regression estimators had undergone series of modification and improvement by several authors using different techniques like power transformation, exponential transformation, linear combination and so forth. Bahl and Tuteja 5 were the first to utilize exponential transformation on ratio and product estimators and thereafter several authors like Singh and Audu, 15 Audu and Singh 4 , Muili et al. 9 , Ishaq et al. 7 , Audu et al. 3 , Singh et al. 14 , Olayiwola et al. 12 , Olayiwola et al. 11 and Audu et al. 2 have used similar approach to enhance the efficiency of estimators of population parameters. Similarly, supplementary variables associated with the study variables have been identified to be helpful in improving the efficiency of ratio, product and regression estimators both at planning and estimation stages. However, the efficiency of these estimators may be affected by data which are characterized by outliers or leverages. Some of the techniques for detecting outliers include Boxplot, Stem and Leaf plot, P-P plot, Euclidean distance, Mahalanobis distance, Hosmer and Lemeshow goodness-of-fit test, Cook's 𝐷 𝑖 . 1 To address the issue of outliers' effects, authors like Kadilar and Cingi 8 , Zaman and Bulut 18 and Zaman 19 have suggested several robust ratio estimators. The current study intends to utilize exponential transformation on Zaman 19 estimators to obtain new estimators with higher efficiency.Zaman and Bulut 18 extended the work of Kadilar and Cingi 8 by inclusion of some slopes' coefficient of other robust regression estimators like Tukey-M, 16 Hampel-M, 6 LMS 13 and LAD 10 in addition to Huber-M 20 used by Kadilar and Cingi 8 and this inclusion leads to new estimators of population mean in the presence of outliers as given below:

Dual-type quantile regression approach for mean estimation incorporating sampled and non-sampled data

“…In a thorough analysis, Begashaw and Yohannes [11] investigated robust regression models for detecting and recognizing outliers. Audu et al [12] employed robust regression techniques to assess how effective exponential-type estimates are for the population mean. Deville and Sarndal [13] significantly advanced the field by offering dependable calibration approach for calculating the mean parameter through probability sampling.…”