A0263
Title: M-quantile regression for zero-inflated data and its applications to small area estimation
Authors: Maria Bugallo - Miguel Hernandez University of Elche (Spain) [presenting]
Domingo Morales - University Miguel Hernandez of Elche (Spain)
Francesco Schirripa - University of Pisa (Italy)
Nicola Salvati - University of Pisa (Italy)
Abstract: Zero-inflated data are almost inevitably complicated by some form of non-observation or inaccurate measurement. From a probabilistic framework, mixtures of GLMMs for the prediction of zero-inflated outcome-dependent indicators have been extensively investigated, and their results are accurate as long as their strong parametric assumptions hold true. However, the demand for results unaffected by outliers in small areas has encouraged the development of new robust inference techniques in recent years. Prompted by the need to develop robust models for variables with an implausible number of zeros, the definition of M-quantiles and their applications are generalized to small area estimation in this field. The contribution includes the proposal of zero-inflated M-quantiles and M-quantile models, the study of asymptotic properties, the derivation of robust predictors, their optimal bias correction and the analytical calculation of mean squared errors. The new methodology is evaluated by means of model-based simulations, showing the gain that the new proposal brings in the presence of just a few atypical data. An application to the Spanish Living Conditions Survey is concluded with.
