Maximum likelihood estimation from complex sample surveys

Maximum likelihood estimation from complex sample data requires additional modeling due to the information in the sample selection. Alternatively, pseudo maximum likelihood methods that consist of maximizing estimates of the census score function can be applied. In this article we review some of the approaches considered in the literature and compare them with a new approach derived from the ideas of ‘weighted distributions’. The focus of the comparisons is on situations where some or all of the design variables are unknown or misspecified. The results obtained for the new method are encouraging, but the study is limited so far to simple situations.