Uniform consistency of automatic and location-adaptive delta-sequence estimators
The class of delta-sequence estimators for a probability density includes the kernel, histogram and orthogonal series types, because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter. There are two important extensions of this class. The first allows a random smoothing parameter, for example that specified by a cross-validation method. The second allows the smoothing parameter to be a function of location, for example an estimator based on nearest-neighbor distance. In this paper a general method is presented which establishes uniform consistency for all of these estimators.
scientific article; zbMATH DE number 4050765
scientific article