Abstract
Abstract Estimators based on linear models are the standard in finite population estimation. However, many items collected in surveys are better described by nonlinear models; these include variables that have binary, binomial, or multinomial distributions. We extend previous work on generalized difference, model-calibrated, and pseudo-empirical likelihood estimators to two-stage cluster sampling and derive their theoretical properties with particular emphasis on multinomial data. We present asymptotic theory for both the point estimators of totals and their variance estimators. The alternatives are tested via simulation using artificial and real populations. The two real populations are one of educational institutions and degrees awarded and one of owned and rented housing units.
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