On weighted local fitting and its relation to the Horvitz-Thompson estimator

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

Abstract

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.

• Dokumententyp: Paper
• Keywords: Bias reduction, nonparametric smoothing, local polynomial modelling, kernel smoothing, leverage values, Horvitz-Thompson theorem, stratification
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch