A minimum variance unbiased estimator of finite population variance using auxiliary information

Archana Panigrahi; Priyaranjan  Dash; Gopabandhu Mishra

doi:https://doi.org/10.59139/stattrans-2025-035

A minimum variance unbiased estimator of finite population variance using auxiliary information

Archana Panigrahi Ravenshaw University, Cuttack, Odisha, India ORCID:https:// orcid.org/ 0009-0006-3349-9524 , Priyaranjan Dash Utkal University, Vanivihar, Bhubaneswar, Odisha, India ORCID:https:// orcid.org/ 0000-0001-6561-4095 , Gopabandhu Mishra Utkal University, Vanivihar, Bhubaneswar, Odisha, India ORCID:https:// orcid.org/ 0000-0003-3959-2333 Statistics in Transition new series, vol. 26, 2025, 3, pages: 209-221 Published online: 5 September 2025 https://doi.org/10.59139/stattrans-2025-035 Citation: Panigrahi A., Dash P., Mishra G., 2025. A minimum variance unbiased estimator of finite population variance using auxiliary information. Statistics in Transition new series, 26(3), pp. 209-221 https://doi.org/10.59139/stattrans-2025-035

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ABSTRACT

A class of estimators of finite population variance (S_y^2) using auxiliary information has been proposed under simple random sampling without replacement (SRSWOR) scheme. An attempt has been made to derive the minimum variance unbiased estimator of finite population variance from the proposed class of unbiased estimators. The efficiency of the class of estimators under optimality is compared with the usual unbiased estimator (t_{V0}=s_y^2), ratio type estimator (t_{VR}), product type estimator{\ (t}_{VP}), regression type estimator {(t}_{Vlr}), exponential ratio type estimator{\ (t}_{VER}), exponential product type estimator {\ (t}_{VEP}), and ratio-in-regression estimator (t_s), both theoretically and empirically under general conditions and under bivariate normality. The proposed class of estimator performs better than these estimators under certain realistic conditions. The proposed class of estimators is generalized for the case of multi-auxiliary variables.

KEYWORDS

simple random sampling without replacement (SRSWOR), unbiased estimator, auxiliary variable, population variance, efficiency

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