Improving the Precision of Population Mean Estimator in Two-Phase Sampling
Archana Panigrahi
Department of Statistics, Ravenshaw University, Cuttack-753003, Odisha, India.
Sanjit Kumar Mohanty *
Department of Mathematics, B.S. Degree College, Jajpur-754296, Odisha, India.
*Author to whom correspondence should be addressed.
Abstract
The use of auxiliary information at the estimation stage improves the precision of estimators in sampling survey methods. The ratio estimators (product estimators) are recommended when there exists a positive correlation (negative correlation) between the study variable and auxiliary variable. When the linear relationship is not very strong, it is preferred to use exponential estimators. The study aims to develop improved product-type estimators for estimating the finite population mean in a two-phase sampling scheme. A product estimator is more efficient than the mean per unit estimator when there exists a negative correlation between the study variable and auxiliary variable. When the population mean of the auxiliary variable is not known in advance, one can use a two-phase sampling scheme or a double sampling scheme. It has been considered that the second-phase sample is directly selected from the population of size N and is independent of the first-phase sample. Some improved product type estimators of finite population mean \(\bar{Y}\) under simple random sampling without replacement a two-phase sampling scheme has been proposed. The efficiency of the proposed product type estimators is compared with the mean per unit estimator, the conventional two-phase product estimator, and the two-phase product type exponential estimator suggested theoretically and empirically.
Keywords: Two-phase sampling, study variable, auxiliary variable, product type estimators, efficiency