Speaker: Dr. S. Rao Jammalamadaka, UC Santa Barbara

Title: Generalized Spacings Estimators

Abstract:

Spacings, which are the gaps between successive observations, have been utilized in statistical inference both for estimation and in testing of hypotheses. After a brief review of this area, we introduce estimators based on higher-order or multi-step spacings, called the “Generalized Spacings Estimators (GSEs)”. Such estimators are obtained by minimizing the so-called Csiszar divergence between the empirical and the true distributions. Maximum likelihood estimators (MLEs) can be viewed as a special case, and GSEs are clearly needed when the MLEs do not exist. Current results generalize much of the earlier work on spacings-based estimation. These estimators are shown to be consistent as well as asymptotically normal under quite general conditions. When the step size and the number of spacings grow with the sample size, an asymptotically efficient class of estimators, called the “Minimum Power Divergence Estimators,” are shown to exist. Simulation studies show that these asymptotically efficient estimators, perform very well in finite samples relative to the MLEs, and unlike the MLEs, are quite robust even under heavy contamination.