Estimating the finite population total under frame imperfections and nonresponse

When sampling from a finite population the access to a good sampling frame is of vital importance. However, the statistician often has to face the problem with non-negligible frame imperfections, e.g. overcoverage and undercoverage. More so, error from nonresponse is an increasing problem in many surveys today. <p> In this paper we discuss different approaches to deal with these problems simultaneously. In particular, we address the situation when there exists a new up-to-date current register and the improvement this brings along.