Title: Optimal generalised Searls estimation procedure of population mean under ranked set sampling scheme

Authors: Dinesh K. Sharma; S.K. Yadav

Addresses: Department of Business, Management and Accounting, University of Maryland Eastern Shore, Princess Anne, MD 21853, USA ' Department of Statistics, Babasaheb Bhimrao Ambedkar University (A Central University), Lucknow, India

Abstract: Searls (1964) concluded that some constant multiple of a sample mean is an improved estimator of the study variable's population mean. Further, it is well established that the proper use of auxiliary information elevates the estimator's efficiency. In this study, a novel, more generalised family of Searls type estimators is suggested to enhance the estimation of the main variable's population mean utilising known auxiliary parameters under ranked set sampling (RSS) scheme. The bias and mean squared error (MSE) expressions are studied up to first-order approximation. The optimal values of Searls constants are derived, which minimises the MSE of the introduced estimator. The minimum MSE of the proposed estimator is also obtained. The introduced family of estimators is compared with the competing estimators of the population mean. The efficiency conditions of the proposed class over the competing estimators are also derived. These efficiency conditions are verified through numerical and simulation studies. The comparison is made based on the estimators' MSEs, and the estimator with the least MSE is recommended for practical applications.

Keywords: ranked set sampling; RSS; main variable; auxiliary variable; Searls estimation; bias; mean squared error; MSE; percentage relative efficiency.

DOI: 10.1504/IJMOR.2022.122211

International Journal of Mathematics in Operational Research, 2022 Vol.21 No.3, pp.305 - 320

Received: 23 Nov 2020
Accepted: 04 Jan 2021
Published online: 12 Apr 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article