Scott, David W.2013-09-162013-09-162013-09-162013-09-162013-052013-09-16May 2013Silver, Justin. "Robust Parametric Functional Component Estimation Using a Divergence Family." (2013) Diss., Rice University. <a href="https://hdl.handle.net/1911/72039">https://hdl.handle.net/1911/72039</a>.https://hdl.handle.net/1911/72039The 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 alpha. Basu noted that only values of alpha in the [0,1] range were of interest -- with alpha = 0 giving the maximum likelihood solution and alpha = 1 the L2E solution (Scott, 2001). As alpha 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 alpha-divergence function to a multivariate partial density component model (Scott, 2004). The usefulness of alpha values greater than 1 will be explored, and the new estimator will be applied to simulated cases and applications in parametric density estimation and regression.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.RobustRobust parametric estimationDivergenceDivergence familyThesis2013-09-16123456789/ETD-2013-05-462