Estimation from an Under-Covered Sample in a Complex Survey for Auditing

Abstract

We encounter a practical problem when from a finite population a complex survey design justifies selection of a sample in five stages. The design stipulates selecting a specified number of n(> 2) first stage units by Rao, Hartley and Cochran's (RHC, 1962) scheme followed by simple random sampling (SRS) without replacement (WOR) in each of the four subsequent stages. At the implementation stage a resource crunch calls for reducing the first stage sample size from n to m (m < n). The consequential modifications in the methods of estimation of population total, mean and ratio of two totals and those of the variance of the first and the mean square errors of the latter two estimators are spelt out. The problem arises in the context of designing audits of Government documents by appropriate sampling.