On weighted local fitting and its relation to the Horvitz-Thompson estimator - Jochen Einbeck; Thomas Augustin (Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen, 2005)
Weighting is a largely used concept in many fields of statistics and has frequently cause 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,
urn:nbn:de:bvb:19-epub-1834-7
Keywords: 519; Bias reduction; nonparametric smoothing; local polynomial modelling; kernel smoothing : leverage values; Horvitz-Thompson theorem; stratification