Comparison of ratio estimators in two-phase sampling

Abstract

To estimate the finite population mean,\(\bar Y\), a two-phase sample may be selected. A simple random sample of sizen′ is chosen, and a concomitant variable,X, is measured for all units. Then, a simple random subsample of sizen (0<n≦n′) is chosen, andY is measured. Seven ratio-type estimators of\(\bar Y\) are given, and their biases and mean square errors determined toO((n′)−2). Then, the estimators are compared (a) without any assumptions about the relation betweenY andX, and (b) assuming thatY andX are linearly related.