Generalized Ratio-cum-Product Estimator for Finite Population Mean under Two-Phase Sampling Scheme

A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The empirical study is also performed to supplement the claim that the developed estimators are more efficient.

A Simple Random Sampling Modified Dual to Product Estimator for Estimating Population Mean using Order Statistics

Bandopadhyaya (1980) developed a dual to product estimator using robust modified maximum likelihood estimators (MMLE’s). Their properties were obtained theoretically and supported through simulations studies with generated as well as one real data set. Robustness properties in the presence of outliers and confidence intervals were studied.

Modified Ratio-Cum-Product Estimators of Population Mean Using Two Auxiliary Variables

A percentile is one of the measures of location used by statisticians showing the value below which a given percentage of observations in a group of observations fall. A family of ratio-cum-product estimators for estimating the finite population mean of the study variable when the finite population mean of two auxiliary variables are known in simple random sampling without replacement (SRSWOR) have been proposed. The main purpose of this study is to develop new ratio-cum-product estimators in order to improve the precision of estimation of population mean in sample random sampling without replacement using information of percentiles with two auxiliary variables. The expressions of the bias and mean square error (MSE) of the proposed estimators were derived by Taylor series method up to first degree of approximation. The efficiency conditions under which the proposed ratio-cum-product estimators are better than sample man, ratio estimator, product estimator and other estimators considered in this study have been established. The numerical and empirical results show that the proposed estimators are more efficient than the sample mean, ratio estimator, product estimator and other existing estimators.

Modified product estimator under two–phase sampling

In this paper, modification of product estimator under two-phase sampling was suggested. The modified product estimator was obtained through transformation in two cases using sample mean of auxiliary variables. Case one was when the second sample was drawn from the first sample while case two was when the second sample was drawn from the population. The bias and mean square error (MSE) of the modified product estimator was obtained. The theoretical and numerical validity of the modified product estimator under the two cases were determined to show it superiority to some considered existing product estimators. Numerical results shows that the modified product estimator under the two cases were more efficient than the considered existing estimators.Keywords: Product estimator, Two-Phase Sampling, Bias, Mean Square Error