The shape of local averaging regions, not just their size, determines whether a local regression estimator achieves the minimax rate, and a single condition called shape regularity is both necessary and sufficient.
Consistency of random forests and other averaging classifiers
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On the pointwise and sup-norm errors for local regression estimators
The shape of local averaging regions, not just their size, determines whether a local regression estimator achieves the minimax rate, and a single condition called shape regularity is both necessary and sufficient.