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Abstract:

DARP Paper
Robust Estimation of Income Distribution Models with Grouped Data, (revised version published in the Journal of the American Statistical Association 92 (1997), pp. 333-340)
Elvezio Ronchetti and Maria-Pia Victoria-Feser June 1996
Paper No' DARP 019:


Tags: diagnostics; grouping effects; influence function; local shift sensitivity; m-estimators; minimum hellinger distance estimators; minimum power divergence estimators; optimal b-robust estimators.

An important aspect of income distribution is the modelling of the data using an appropriate parametric model. This involves estimating the parameters of the models, given the data at hand. Income data are typically in grouped form. Moreover, they are not always reliable in that they may contain contamination. Classical estimation procedures with grouped data are now widely available, but are typically not robust in that a small amount of contaminated data can considerably bias the estimation. In this paper we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators and other well known classical estimators. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore we propsose a more general class of estimators which allow us to construct robust procedures. We define optimal bounded influence function estimators and by a simulation study, we show that under small model contaminations, they are more stable than the classical estimators for grouped data. Finally, our results are applied to a particular real example.