Improvement Over Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean of the study variable y, we propose a ratio‐type estimator which gives an improvement over estimators given by Upadhyaya and Singh (1999), Sisodia and Dwivedi (1981), and Singh and Kakran (1993). These estimators are compared by observing the bias and mean square error (MSE). In this empirical study, the suggested estimator under the optimal condition is found to be more efficient than the estimators mentioned above.     

A General Class of Ratio‐Type Estimators Under Super‐Population Model

The problem of constructing classes of estimators for population mean has been widely discussed by various authors under design approach in sample surveys. An attempt by Upadhyaya , Singh , and Vos (1985) has been made to combine the usual mean and ratio estimator with suitable weights in order to define a general class of estimators. This paper is an attempt to study properties of the same estimator under super‐population model. Optimum weights have also been proposed. Results have been supported with some numerical examples.     

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y- of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y-, the ratio estimator y-_R = y-X-/x-, Sisodia and Dwivedi (1981) estimator y-_s = y-(X- + C_x)/(x- + C_x) and Singh and Kakran (1993) estimator y-_k = y[X- + β₂(x)]/[x- + β₂(x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.     

A Generalized Class of Synthetic Estimators with Application to Crop Acreage Estimation for Small Domains

This paper defines and discusses a generalized class of synthetic estimators for small domains, using auxiliary information, under simple random sampling and stratified random sampling schemes. The generalized class of synthetic estimators, among others, includes the simple, ratio and product synthetic estimators. The proposed class of synthetic estimators gives consistent estimators if the synthetic assumption holds. Further, it demonstrates the use of the generalized synthetic and ratio synthetic estimators for estimating crop acreage for small domains and also compare their relative performance with direct estimators, empirically, through a simulation study.     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.