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

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

• Item Type: Paper (Research Paper)
• Keywords: Bias reduction, nonparametric smoothing, local polynomial modelling, kernel smoothing, leverage values, Horvitz-Thompson theorem, stratification
• Collections: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics