Houston, TX 77005
3:30 p.m. Wednesday, April 3, 2013
On Campus | Alumni
The classical parametric estimation approach, maximum likelihood, while providing maximally efficient estimators at the correct model, lacks robustness. As a modification of maximum likelihood, Huber (1964) introduced M-estimators, which are very general but often ad hoc. Basu et al. (1998) developed a family of density-based divergences, many of which exhibit robustness. It turns out that maximum likelihood is a special case of this general class of divergence functions, which are indexed by a parameter ?. Basu noted that only values of ? between 0 and 1 were of interest – with ? = 0 yielding the maximum likelihood solution and ? = 1 the L2E solution (Scott, 2001). As ? increases, there is a clear tradeoff between increasing robustness and decreasing efficiency. This thesis develops a family of robust location and scale estimators by applying Basu’s ?-divergence function to a multivariate partial density component model (Scott, 2003). The usefulness of ? values greater than 1 will be explored, and the new estimators will be applied to simulated cases and applications in parametric density estimation and regression.