Abstract
To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.