Title: Advanced class for variance estimation utilising known quartiles of the auxiliary variable

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

Addresses: Department of Business, Management and Accounting, University of Maryland Eastern Shore, Princess Anne, MD 21853, USA ' Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, U.P., India ' Department of Accounting and Finance, Virginia State University, Singleton Hall, VA 23806, USA

Abstract: Variance is a natural phenomenon among similar objects in nature and it is one of the measures of dispersion. Therefore, its estimation is of crucial importance for large populations to save time, money and manpower. In this paper, we propose an estimator for estimating population variance of the primary (study) variable using known quartiles of the secondary (auxiliary) variable and their functions. The optimum value of the scalar in the suggested estimator is acquired to ensure mean squared error (MSE) of the suggested estimator as a minimum. A comparison has been presented between suggested and the competing estimators, and the theoretical efficiency conditions are derived. For the verification of these efficiency conditions through the calculation of mean square errors of various estimators, a numerical study is performed.

Keywords: main variable; auxiliary variable; variance estimator; bias; MSE; PRE.

DOI: 10.1504/IJAMS.2021.117437

International Journal of Applied Management Science, 2021 Vol.13 No.3, pp.226 - 239

Received: 09 May 2019
Accepted: 25 Jul 2019
Published online: 07 Sep 2021 *

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