Estimating the finite population total under Frame imperfections

When sampling from a finite population the access to a good samplingcframe is of vital importance. However, the statistician often has to confront the problem of estimation in the face of non-negligible frame imperfections, e.g. overcoverage and undercoverage. In this paper we <p> discuss different approaches to deal with this problem. In particular, we address the situation when there exists a new up-to-date current <p> register and the improvement this brings along. The paper is part of a project which eventually aims at developing approaches for handling <p> the estimation problem when nonresponse and frame imperfection occur simultaneously.