# Density estimation with quadratic loss: a confidence intervals method

ESAIM: Probability and Statistics (2008)

- Volume: 12, page 438-463
- ISSN: 1292-8100

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topAlquier, Pierre. "Density estimation with quadratic loss: a confidence intervals method." ESAIM: Probability and Statistics 12 (2008): 438-463. <http://eudml.org/doc/250397>.

@article{Alquier2008,

abstract = {
We propose a feature selection method for density estimation with
quadratic loss. This method relies on the study of unidimensional
approximation models and on the definition of confidence regions for
the density thanks to these models. It is quite general and includes
cases of interest like detection of relevant wavelets coefficients
or selection of support vectors in SVM. In the general case, we
prove that every selected feature actually improves the performance
of the estimator. In the case where features are defined by
wavelets, we prove that this method is adaptative near minimax (up
to a log term) in some Besov spaces. We end the paper by
simulations indicating that it must be possible to extend the
adaptation result to other features.
},

author = {Alquier, Pierre},

journal = {ESAIM: Probability and Statistics},

keywords = {Density estimation; support vector machines; kernel algorithms;
thresholding methods; wavelets; density estimation; thresholding methods},

language = {eng},

month = {7},

pages = {438-463},

publisher = {EDP Sciences},

title = {Density estimation with quadratic loss: a confidence intervals method},

url = {http://eudml.org/doc/250397},

volume = {12},

year = {2008},

}

TY - JOUR

AU - Alquier, Pierre

TI - Density estimation with quadratic loss: a confidence intervals method

JO - ESAIM: Probability and Statistics

DA - 2008/7//

PB - EDP Sciences

VL - 12

SP - 438

EP - 463

AB -
We propose a feature selection method for density estimation with
quadratic loss. This method relies on the study of unidimensional
approximation models and on the definition of confidence regions for
the density thanks to these models. It is quite general and includes
cases of interest like detection of relevant wavelets coefficients
or selection of support vectors in SVM. In the general case, we
prove that every selected feature actually improves the performance
of the estimator. In the case where features are defined by
wavelets, we prove that this method is adaptative near minimax (up
to a log term) in some Besov spaces. We end the paper by
simulations indicating that it must be possible to extend the
adaptation result to other features.

LA - eng

KW - Density estimation; support vector machines; kernel algorithms;
thresholding methods; wavelets; density estimation; thresholding methods

UR - http://eudml.org/doc/250397

ER -

## References

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