Metrika 2000) 51: 267±276 > Springer-Verlag 2000 Compromised imputation in survey sampling Sarjinder Singh1, Stephen Horn2 1 Department of Mathematics and Statistics, University of Southern Maine, Portland, Maine, ME 04101-9300, USA E-mail: sarjinder@yahoo.com) 2 Department of Family and Community Services, Box 7788, Canberra Mail Centre, ACT 2610, Australia E-mail: stephen.horn@facs.gov.au) Received: July 1998 Abstract. In this paper, a compromised imputation procedure has been suggested. The estimator of mean obtained from compromised imputation remains better than the estimators obtained from ratio method of imputation and mean method of imputation. An idea to form ``Warm Deck Method'' of imputation has also been suggested. Key words: Estimation of mean, missing data, imputation, ratio estimator, bias, mean squared error, design based approach. 1. Introduction Missing data is a common problem in sample surveys and imputation is fre- quently used to substitute values for missing data. Statisticians have recognised for some time that failure to account for the stochastic nature of incomplete- ness in the form of missingness of data can spoil inference. A natural question arises what one needs to assume to justify ignoring the incomplete mechanism. Rubin 1976) addressed three concepts: missing at random MAR), observed at random OAR) and parameter distribution PD). Rubin de®ned ``The data are MAR if the probability of the observed missingness pattern, given the observed and unobserved data, does not depend on the value of the un- observed data''. Heitzan and Basu 1996) have distinguished the meaning of missing at random MAR) and missing completely at random MCAR) in a very nice way. Following them, we implicitly assume MCAR in the present investigation. Let Y  N 1 P N i1 y i be the mean of the ®nite population W f1; 2; ... ; i; ... ; N g. A simple random sample without replacement SRSWOR), s, of size n is drawn from W to estimate Y . Let r be the number of responding units out of sampled n units. Let the set of responding units be