MAXIMUM-LIKELIHOOD INFERENCE FROM SAMPLE SURVEY DATA

In this paper we present a general theory for maximum likelihood inference based on sample survey data. Our purpose is to identify and emphasise the recurring basic concepts that arise in the application of likelihood methods, including the estimation of precision, to survey data. We discuss the problems generated by the effects of sample design, selection and response processes. We also discuss the problem of failures of the model assumptions and the role of sample inclusion probabilities in achieving robustness. We present two illustrative examples, one of which illustrates the use of non-Gaussian models.