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Mixing Strategies for Density Estimation
 Ann. Statist
"... General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under KullbackLeibler and square L 2 losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by m ..."
Abstract

Cited by 54 (9 self)
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General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under KullbackLeibler and square L 2 losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks. A consequence is that under some mild conditions, an asymptotically minimaxrate adaptive estimator exists for a given countable collection of density classes, i.e., a single estimator can be constructed to be simultaneously minimaxrate optimal for all the function classes being considered. A demonstration is given for highdimensional density estimation on [0; 1] d where the constructed estimator adapts to smoothness and interactionorder over some piecewise Besov classes, and is consistent for all the densities with finite entropy. 1. Introduction. In Recent years, there has been an increasing interest in adaptive fu...
Combining Different Procedures for Adaptive Regression
 Journal of Multivariate Analysis
, 1998
"... Given any countable collection of regression procedures (e.g., kernel, spline, wavelet, local polynomial, neural nets, etc), we show that a single adaptive procedure can be constructed to share the advantages of them to a great extent in terms of global squared L 2 risk. The combined procedure basic ..."
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Cited by 51 (9 self)
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Given any countable collection of regression procedures (e.g., kernel, spline, wavelet, local polynomial, neural nets, etc), we show that a single adaptive procedure can be constructed to share the advantages of them to a great extent in terms of global squared L 2 risk. The combined procedure basically pays a price only of order 1=n for adaptation over the collection. An interesting consequence is that for a countable collection of classes of regression functions (possibly of completely different characteristics), a minimaxrate adaptive estimator can be constructed such that it automatically converges at the right rate for each of the classes being considered.
Model selection for nonparametric regression.
 Statist. Sinica
, 1999
"... Abstract: Risk bounds are derived for regression estimation based on model selection over an unrestricted number of models. While a large list of models provides more flexibility, significant selection bias may occur with model selection criteria like AIC. We incorporate a model complexity penalty ..."
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Cited by 25 (13 self)
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Abstract: Risk bounds are derived for regression estimation based on model selection over an unrestricted number of models. While a large list of models provides more flexibility, significant selection bias may occur with model selection criteria like AIC. We incorporate a model complexity penalty term in AIC to handle selection bias. Resulting estimators are shown to achieve a tradeoff among approximation error, estimation error and model complexity without prior knowledge about the true regression function. We demonstrate the adaptability of these estimators over full and sparse approximation function classes with different smoothness. For highdimensional function estimation by tensor product splines we show that with number of knots and spline order adaptively selected, the least squares estimator converges at anticipated rates simultaneously for Sobolev classes with different interaction orders and smoothness parameters.