Statistics and Applications Volume 10, Nos. 1&2, 2012 (New Series), pp. 13-25 Estimation of Domain Total for Unknown Domain Size in the Presence of Nonresponse Kaustav Aditya, U.C. Sud and Hukum Chandra Indian Agricultural Statistics Research Institute, New Delhi, India ________________________________________________________________________ Abstract This article describes the estimation of domain total in the presence of nonresponse when the domain size unknown and the sampling design is two-stage. Further, the response mechanism is assumed to be deterministic. An estimator based on sub-sampling of non-respondents, collecting data on the sub-sample through specialized efforts, is proposed. Expression for the variance of the estimator is also developed. A suitable cost function is considered for obtaining the optimum sample sizes. Empirical studies are carried out to examine the percentage reduction in the expected cost of proposed estimator. Keywords: Cost function; Nonresponse; Sub-sample; Two-stage sampling ________________________________________________________________________ 1 Introduction For large or medium scale surveys we are often faced with the scenario that the sampling frame of ultimate stage units is not available and the cost of construction of the frame is very high. Sometimes the population elements are scattered over a wide area resulting in a widely scattered sample. Therefore, not only the cost of enumeration of units in such a sample may be very high, the supervision of field work may also be very difficult. For such situations, two-stage or multi-stage sampling designs are very effective. It is also the case that, in many human surveys, information is not obtained from all the units in surveys. The problem of nonresponse persist even after call backs. The estimates obtained from incomplete data may be biased particularly when the respondents differ from the non-respondents. Hansen and Hurwitz (1946) proposed a technique for adjusting for nonresponse to address the problem of bias. The technique consists of selecting a sub-