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Einbeck, Jochen; Augustin, Thomas (2005): On weighted local fitting and its relation to the Horvitz-Thompson estimator. Collaborative Research Center 386, Discussion Paper 465


Weighting is a largely used concept in many fields of statistics and has frequently caused controversies on its justification and profit. In this paper, we analyze a weighted version of the well-known local polynomial regression estimators, derive their asymptotic bias and variance, and find that the conflict between the asymptotically optimal weighting scheme and the practical requirements has a surprising counterpart in sampling theory, leading us back to the discussion on Basu's (1971) elephants.