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Kernel Density Estimation with Generalized Binning
Author(s) -
Pawlak M.,
Stadtmuller U.
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00167
Subject(s) - mathematics , estimator , multivariate kernel density estimation , kernel density estimation , variable kernel density estimation , kernel (algebra) , quantile , statistics , kernel smoother , kernel method , mean squared error , kernel embedding of distributions , combinatorics , radial basis function kernel , artificial intelligence , computer science , support vector machine
We propose kernel density estimators based on prebinned data. We use generalized binning schemes based on the quantiles points of a certain auxiliary distribution function. Therein the uniform distribution corresponds to usual binning. The statistical accuracy of the resulting kernel estimators is studied, i.e. we derive mean squared error results for the closeness of these estimators to both the true function and the kernel estimator based on the original data set. Our results show the influence of the choice of the auxiliary density on the binned kernel estimators and they reveal that non‐uniform binning can be worthwhile.