Title: Optimal Searls estimation of population variance under a systematic sampling scheme: a simulation study

Authors: S.K. Yadav; Dinesh K. Sharma; Abhishek Yadav; Surendra Kumar

Addresses: Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow – 226025, India ' Department of Business, Management and Accounting, University of Maryland Eastern Shore, Princess Anne, MD, 21853, USA ' Department of Civil Engineering, UIET, Babasaheb Bhimrao Ambedkar University, Lucknow – 226025, India ' Department of Mathematics, Govt. Degree College Pihani, Hardoi – 241406, India

Abstract: This paper proposes an improved estimation of population variance using known auxiliary information in a systematic sampling scheme. To enhance population variance estimation, we suggest a Searls (1964) type estimator using known auxiliary parameters. The bias and mean square error (MSE) are derived up to an approximation of first degree. The optimal values of the Searls characterising constants are obtained, and the corresponding least mean squared errors are also obtained. The suggested estimators are theoretically compared with the competing estimators. The efficiency conditions of the suggested estimators over competing estimators are obtained. The theoretical efficiencies are verified using a real primary dataset collected from a block of Barabanki District in Uttar Pradesh State, India. The estimator with a lesser MSE or higher percentage relative efficiency (PRE) is preferred for elevated population variance estimation in a systematic random sampling scheme.

Keywords: study variable; auxiliary variable; systematic sampling; bias; MSE; mean square error; PRE; percentage relative efficiency.

DOI: 10.1504/IJCSM.2022.128186

International Journal of Computing Science and Mathematics, 2022 Vol.16 No.3, pp.239 - 251

Received: 03 Aug 2020
Accepted: 03 Sep 2020
Published online: 11 Jan 2023 *

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