Some diagnostics and influence analysis tools for small area estimation models

This paper discusses some relevant questions about the diagnostics for small area estimation basic models. The main characteristics and employments of that models suggest to investigate in deep how traditional mixed model diagnostics can be addressed to analyze some special questions in small area estimation. We investigate what type of problems are of interest for survey practitioners, and applied statisticians in general. In fact, traditional tools for mixed models can be evaluated and treated by the particular point of view of survey statisticians. For instance, these methods can be upgraded by the analysis of the influence on the estimation of the mean squared error of the Eblup. The main issues are discussed starting from some approximations of the restricted maximum likelihood estimators, in order to get closed-form solutions of the variance parameters estimates. We investigate the problem of the leverage of observed values on predicted values by the Eblup, as well as the general problem of the influence on the model estimates. Starting from the consideration that the whole diagnostics in mixed models depends on the estimates of the variance parameters, we discuss the problem of the influence in order to coming out the role played by the estimation of the model variance itself. We further provide to analyze the most relevant conclusions of the research on real data, with an application.