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Title: Uniform inference for SAE Authors:  Stefan Sperlich - University of Geneva (Switzerland) [presenting]
Maria Jose Lombardia - Universidade da Coruna (Spain)
Katarzyna Reluga - University of Toronto (Canada)
Abstract: Simultaneous inference is addressed for mixed parameters which are the key ingredients in small area estimation. We assume linear mixed model framework. We analyse statistical properties of a max-type statistic and use it to construct simultaneous prediction intervals as well as to implement multiple testing procedure. In addition, we adapt some of the simultaneous inference methods from regression and nonparametric curve estimation and compare them with our approaches. Simultaneous intervals are necessary to compare areas since the presently available intervals are not statistically valid for such analysis. The proposed testing procedures can be used to validate certain statements about the set of mixed parameters or to test pairwise differences. The proposal is accompanied by simulation experiments and a data example on small area household incomes. They all demonstrate an excellent performance and utility of our techniques.