Statistics Seminars: Smoothing, Sampling, and Basu's elephants
23 October 2007 14:15 in CM221
Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this talk, we analyze design-weighted versions of the well-known local polynomial regression estimators, provide their asymptotic bias and variance, and observe that the asymptotically optimal weights are in conflict with (practically motivated) weighting schemes previously proposed in the literature. We investigate this conflict using theory, simulation, and real data from the environmental sciences, and find that the problem has a surprising counterpart in sampling theory. This leads us back to the discussion on the Horvitz-Thompson estimator and Basu's (1971) elephants. The crucial point is that bias-minimizing weights can make estimators extremely vulnerable to outliers in the design space and have therefore to be used with particular care.
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