New Techniques for Estimating Finite Population Variance Using Ranks of Auxiliary Variable in Two-Stage Sampling

Umer Daraz, Mohammed Ahmed Alomair (), Olayan Albalawi and Abdulaziz S. Al Naim
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Umer Daraz: School of Mathematics and Statistics, Central South University, Changsha 410017, China
Mohammed Ahmed Alomair: Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Olayan Albalawi: Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Abdulaziz S. Al Naim: Accounting Department, Business School, King Faisal University, Al-Ahsa 31982, Saudi Arabia

Mathematics, 2024, vol. 12, issue 17, 1-14

Abstract: This article presents a new set of estimators designed to estimate the finite population variance of a study variable in two-phase sampling. These estimators utilize the information about extreme values and ranks of an auxiliary variable. Through a first-order approximation, we investigate the properties of these estimators, including biases and mean squared errors (MSEs). Furthermore, a comprehensive simulation study is conducted to assess their performance and validate our theoretical insights. Results demonstrate that our proposed class of estimators performs better in terms of percent relative efficiency (PRE) across various simulation scenarios compared to existing estimators. In addition, in the application section, we utilize three data sets to further validate the performance of our proposed estimators against conventional unbiased variance estimators, ratio and regression estimators, as well as other existing methods.

Keywords: exponential estimator; variance estimation; extreme values; ranks; MSE; PRE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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