An Alternative Class of Ratio-Regression-Type Estimator under Two-Phase Sampling Scheme

Abstract

In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square error and percentage relative efficiency. The proposed estimator can be used to estimate the averages of economic variables such as inflation, exchange rate, and standard of living for policy formulation.

The Efficiency of a Ratio Product Estimator in the Estimation of the Finite Population Coefficient of Variation

“…are the population means of the study and auxiliary variables. 2 represents the population variance of the study variable. 2 represents the population variance of the auxiliary variable.…”

“…2 represents the population variance of the study variable. 2 represents the population variance of the auxiliary variable.…”

“…Various estimation strategies have been developed by many researchers in the field of sample surveys for the estimation of population parameters, including ( [1][2][3][4]). Some of the estimation methods use auxiliary information for the precise estimate of the parameter.…”

Combined Exponential-Type Estimators for Finite Population Mean in Two-Phase Sampling

“…Naik and Gupta [12], Zakari et al [13] suggested the classical ratio type estimator of the population mean utilizing the auxiliary attribute under the simple random sampling as (1) Kumar and Bahl [14] suggested a ratio estimator of the population mean utilizing the auxiliary attribute under two-phase sampling as (2) The mean square error (MSE) equations of up to the first order of approximation, for Case-I and Case-II are given respectively as;…”

“…A second-phase sample can then be taken and the study variable y with an auxiliary variable x can be observed. Singh et al [1] and Muhammad et al [2] discussed that the major advantage of using two-phase sampling is the gain in high precision without a substantial increase in cost. Several authors improved ratio and regression estimators by adopting at least one auxiliary variable in two phase sampling scheme.…”