9305573 The proposed research is to study efficient ways of applying maximum likelihood (ML) inference to complex survey data. The methodology we intend to apply is based on the ideas of weighted distributions. It consists of expressing the joint probability density functions (pdf) for units in the sample as products of the sample inclusion probabilities, expressed as functions of the observed data, and the marginal pdf holding in the population. These products are normalized. ML estimators are obtained by maximazing the resulting weighted pdf with respect to the unknown model parameters. Survey data are often used in the social sciences and by government agencies to estimate parameters of interest (e.g. cell frequencies; relationships among variables). Often the survey is complex in the sense that the chance that an individual is in the sample depends on many factors. As illustrated in the statistical and econometric literature, failure to account for the features of the sampling design in the inference process may yield misleading results. The significance of the proposed research is that it will hopefully provide a unified approach for drawing inferences from complex survey data that will account for the known features of the sampling design.
