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. 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.