Affiliations: School of Studies in Statistics, Vikram University, Ujjain, MP, India
Corresponding author: Ramkrishna S. Solanki, School of Studies in Statistics, Vikram University, Ujjain 456010, MP, India. E-mail: [email protected].
Abstract: Starting from the Singh et al.  [Current Science 57: 1331–1334] difference estimator, we define a class of estimators for the unknown variance of a survey variable on the line of Diana et al.  [Stat Methods Appl DOI 10.1007/s10260-010-0156-6] when auxiliary variable is available. The bias and mean square error of the estimators belonging to the class of estimators are derived and the expressions for the optimum parameters minimizing the asymptotic mean square error are given in closed form. A simple condition allowing us to improve the usual difference estimator due to Das and Tripathi  [Sankhya C 40: 139–148] is derived. Finally, in order to judge the merits of some estimators with the usual difference one, an empirical study is carried out.
Keywords: Singh et al. estimator, difference estimator, study variable, bias, mean square error