Small area estimation with categorical outcomes often requires intensive computation, as the marginal likelihood does not have a closed form in general. The likelihood analysis is further complicated by deviations in distributional assumptions often arise through outliers in the data. In this paper, the author proposes a robust method for estimating the small area parameters. Finite-sample properties of the estimators are investigated using Monte Carlo simulations. The empirical study shows that the proposed robust method is very useful for bounding the influence of outliers on the small area estimators. To approximate the mean squared errors of the estimators, a parametric bootstrap method is adopted. An application is also provided using actual data from a public health survey.

Categorical data, Mean squared prediction error, Mixed model, Robust estimation, Small area prediction
School of Mathematics and Statistics

Sinha, S. K. (2019). Robust small area estimation in generalized linear mixed models. Metron. doi:10.1007/s40300-019-00161-6