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On Locally Adaptive Density Estimation
, 1996
"... : In this paper, theoretical and practical aspects of the samplepoint adaptive positive kernel density estimator are examined. A closedform expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning. With this expression, the exact behavio ..."
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Cited by 53 (5 self)
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: In this paper, theoretical and practical aspects of the samplepoint adaptive positive kernel density estimator are examined. A closedform expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning. With this expression, the exact
Adaptative density estimation with dependent observations
, 2005
"... Assume that (Xn)n∈Z is a real valued stationary time series admitting a common density f. To estimate f in an independent and identically distributed setting, Donoho, Johnstone, Kerkyacharian & Picard (1996) proposed a quasiminimax method based on thresholding wavelets. The aim of the present w ..."
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Assume that (Xn)n∈Z is a real valued stationary time series admitting a common density f. To estimate f in an independent and identically distributed setting, Donoho, Johnstone, Kerkyacharian & Picard (1996) proposed a quasiminimax method based on thresholding wavelets. The aim of the present
Adaptive density estimation under dependence
, 2006
"... Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue measure. Donoho et al. (1996) propose a nearminimax method based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of ..."
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Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue measure. Donoho et al. (1996) propose a nearminimax method based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim
Adaptive density estimation under dependence
, 2006
"... Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue measure. Donoho et al. (1996) propose a nearminimax method based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of ..."
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Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue measure. Donoho et al. (1996) propose a nearminimax method based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim
ZeroBias Locally Adaptive Density Estimators
 Journal of the Royal Statistical Society, B (Submitted
, 2000
"... this paper, is referred to as a local density or balloon estimator. The local density estimator varies the bandwidth with the estimation point, i.e. ..."
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Cited by 7 (0 self)
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this paper, is referred to as a local density or balloon estimator. The local density estimator varies the bandwidth with the estimation point, i.e.
Adaptive density estimation: a curse of support?
, 2009
"... This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very difficult to handle in practice. In this work, we show ..."
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Cited by 10 (4 self)
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This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very difficult to handle in practice. In this work, we
Adaptive density estimation using the blockwise Stein method
"... We study the problem of nonparametric estimation of a probability density of unknown smoothness in L2(R). Expressing mean integrated squared error (MISE) in the Fourier domain, we show that it is close to mean squared error in the Gaussian sequence model. Then applying a modified version of Stein’s ..."
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blockwise method, we obtain a linear monotone oracle inequality. Two consequences of this oracle inequality are that the proposed estimator is sharp minimax adaptive over a scale of Sobolev classes of densities, and that its MISE is asymptotically smaller than or equal to that of kernel density estimators
ADAPTIVE DENSITY ESTIMATION UNDER WEAK DEPENDENCE
, 2008
"... Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue’s measure. Donoho et al. (1996) propose nearminimax estimators bfn based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. T ..."
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Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue’s measure. Donoho et al. (1996) propose nearminimax estimators bfn based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting
Results 1  10
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2,272,316