Journal of the Korean Statistical Society 37 (2008) 375–383 www.elsevier.com/locate/jkss Optimal estimation of population variance using equilibrated stratified sampling from infinite populations Mariano Ruiz Espejo a , Housila P. Singh b , Miguel Delgado Pineda c , Saralees Nadarajah d,∗ a UNED and UPCO, Apartado 19207, 28080 Madrid, Spain b Vikram University, Ujjain-456010, M. P., India c Facultad de Ciencias, UNED, 28040 Madrid, Spain d University of Manchester, Manchester, M13 9PL, UK Received 5 January 2008; accepted 1 April 2008 Available online 7 May 2008 Abstract A class of unbiased estimators of the population variance is proposed when the coefficient of variation is known for each stratum. The technique of equilibrated stratification is used. It is shown that, with optimum allocation, the variance of the suggested estimator for sufficiently large sample size is less than that of the classical minimum variance unbiased estimator under distribution- free setting. Other classes of estimators are also given with similar or better practical properties. c  2008 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved. AMS 2000 subject classifications: primary 62D05; secondary 62J10 Keywords: Equilibrated stratification; Optimum allocation; Population variance; Unbiasedness 1. Introduction The problem of estimating the variance of finite populations (particularly, for fixed population and superpopulation models) has been discussed by various authors (see, for example, Chaudhuri (1978), Ericson (1969), Hansen, Hurwitz, and Madow (1953), Liu (1974), Mukhopadhyay (1978, 1982), Singh, Upadhyaya, and Namjoshi (1988), Skinner (1981, 1983) and Wolter (1985)). It should be observed, however, that the variance estimation for stratified sampling has not attracted much attention while the population mean estimation for stratified sampling has been dealt at great length (see, for example, Cochran (1977), Dalenius (1957), Dalenius and Hodges (1959), Raj (1968) and Ruiz-Espejo (1985, 1987)). The estimation of the variance for stratified sampling for infinite populations has been discussed by Ruiz-Espejo and Ruiz-Espejo (1992). Assume that the characteristic Y under study has a continuous probability density function f ( y ), a < y < b. The population mean and the population variance are defined by μ =  b a tf (t )dt ∗ Corresponding author. E-mail address: mbbsssn2@manchester.ac.uk (S. Nadarajah). 1226-3192/$ - see front matter c  2008 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jkss.2008.04.001