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

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.