On optimality of Bayesian testimation in the normal means problem (2007)
Abramovich, Felix, Grinshtein, Vadim, Pensky, Marianna
We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a...
Adapting to unknown sparsity by controlling the false discovery rate (2006)
Abramovich, Felix, Benjamini, Yoav, Donoho, David L., Johnstone, Iain M.
We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways...
Adapting to Unknown Sparsity by controlling the False Discovery Rate (2005)
Abramovich, Felix, Benjamini, Yoav, Donoho, David L., Johnstone, Iain M.
We attempt to recover an $n$-dimensional vector observed in white noise, where $n$ is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different...
On optimality of Bayesian wavelet estimators (2002)
Felix Abramovich, Umberto Amato, Claudia Angelini
We investigate the asymptotic optimality of several Bayesian wavelet estimators corresponding to dierent losses, namely, posterior mean, posterior median and Bayes Factor. The considered prior is a...
Empirical Bayes approach to block wavelet function estimation (2001)
Felix Abramovich, Panagiotis Besbeas, Theofanis Sapatinas
Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coe#cients. However, it has been shown that grouping the...
Empirical Bayes approach to block wavelet function estimation (2000)
Felix Abramovich, Panagiotis Besbeas, Theofanis Sapatinas
Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of empirical wavelet coecients. However, it has been shown that grouping the empirical...
On One-Sided Estimation Of A Sharp Cusp Using Wavelets (2000)
Felix Abramovich, Alexander Samarov
We consider the sharp cusp detection problem in the nonparametric regression setting. We assume that the mth derivative of the unknown function (the function itself for m = 0 in particular) is...
Adaptive Thresholding Of Wavelet Coefficients (2000)
Felix Abramovich, Yoav Benjamini
Wavelet techniques have become an attractive and efficient tool in function estimation. Given noisy data, its discrete wavelet transform is an estimator of the wavelet coefficients. It has been shown...
Adapting to Unknown Sparsity by controlling the False Discovery Rate (2000)
Felix Abramovich, Yoav Benjamini, David Donoho, Iain Johnstone
We attempt to recover a high-dimensional vector observed in white noise, where the vector is known to be sparse, but the degree of sparsity is unknown. We consider three di#erent ways of defining...
Adapting to Unknown Sparsity by controlling the False Discovery Rate (2000)
Felix Abramovich, Yoav Benjamini, David Donoho, Iain Johnstone
We attempt to recover a high-dimensional vector observed in white noise, where the vector is known to be sparse, but the degree of sparsity is unknown. We consider three dierent ways of dening...
Improved Inference In Nonparametric Regression Using (1999)
Felix Abramovich, David M. Steinberg
Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (1978,1983) showed that smoothing splines are also Bayes estimates and used the corresponding prior model...
Felix Abramovich, Vadim Grinshtein
We consider first the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be...
Bayesian Approach To Wavelet Decomposition and Shrinkage (1999)
Felix Abramovich, Theofanis Sapatinas
We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function's regularity can be incorporated into a prior model for its wavelet coefficients by establishing a...
Adaptive Thresholding Of Wavelet Coefficients (1999)
Felix Abramovich, Yoav Benjamini
Wavelet techniques have become an attractive and efficient tool in function estimation. Given noisy data, its discrete wavelet transform is an estimator of the wavelet coefficients. It has been shown...
Some statistical remarks on the derivation of BER in amplified optical communication systems (1999)
Felix Abramovich, Polina Bayvel
We consider the signal detection problem in amplified optical transmission system as a statistical hypothesis testing procedure and show that the detected signal has a well known chi-squared...
Felix Abramovich, Yoav Benjamini
Given noisy signal, its finite discrete wavelet transform is an estimator of signal's wavelet expansion coefficients. An appropriate thresholding of coefficients for further reconstruction of...
Wavelet Analysis and Its Statistical Applications (1999)
Felix Abramovich, Trevor C. Bailey, Theofanis Sapatinas
In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be...
Wavelet Analysis and Its Statistical Applications (1999)
Felix Abramovich, Trevor C. Bailey, Theofanis Sapatinas
In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be...
Derivation of equivalent kernel for general spline smoothing: a systematic approach (1999)
Abramovich, Felix, Grinshtein, Vadim
We consider first the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be...
Bayesian Approach To Wavelet Decomposition and Shrinkage (1999)
Felix Abramovich, Theofanis Sapatinas
We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function's regularity can be incorporated into a prior model for its wavelet coefficients by establishing a...
Wavelet Analysis and Its Statistical Applications (1999)
Felix Abramovich, Trevor C. Bailey, Theofanis Sapatinas
In recent years there has been considerable development in the use of wavelet methods in statistics and this is an interesting time to look at the variety of applications in which such methods might...
Wavelet Analysis and Its Statistical Applications (1999)
Felix Abramovich, Trevor C. Bailey, Theofanis Sapatinas
In recent years there has been considerable development in the use of wavelet methods in statistics and this is an interesting time to look at the variety of applications in which such methods might...
Bayesian Approach To Wavelet Decomposition and Shrinkage (1999)
Felix Abramovich, Theofanis Sapatinas
We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function's regularity can be incorporated into a prior model for its wavelet coefficients by establishing a...
Thresholding Of Wavelet Coefficients As Multiple Hypotheses Testing Procedure (1997)
Felix Abramovich, Yoav Benjamini
Given noisy signal, its finite discrete wavelet transform is an estimator of signal's wavelet expansion coefficients. An appropriate thresholding of coefficients for further reconstruction of...
Adaptive Thresholding Of Wavelet Coefficients (1997)
Felix Abramovich, Yoav Benjamini
Wavelet techniques have become an attractive and efficient tool in function estimation. Given noisy data, its discrete wavelet transform is an estimator of the wavelet coefficients. It has been shown...
Some statistical remarks on the derivation of BER in amplified optical communication systems (1997)
Felix Abramovich, Polina Bayvel
We consider the signal detection problem in amplified optical transmission system as a statistical hypothesis testing procedure and show that the detected signal has a well known chi-squared...
Improved Inference In Nonparametric Regression Using L_k-Smoothing Splines (1997)
Felix Abramovich, David M. Steinberg
Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (1978,1983) showed that smoothing splines are also Bayes estimates and used the corresponding prior model...
The Vaguelette-Wavelet Decomposition Approach To Statistical Inverse Problems (1996)
Felix Abramovich, Bernard W. Silverman
A wide variety of scientific settings have to do with indirect noisy measurements. We are interesting in some object f(t) but the data is accessible only about some transform (Kf)(t), where K is some...
On Optimality of Bayesian Wavelet Estimators
Felix Abramovich, Umberto Amato, Claudia Angelini
We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a...
Empirical Bayes approach to block wavelet function estimation
Abramovich, Felix, Besbeas, Panagiotis, Sapatinas, Theofanis
Pointwise optimality of Bayesian wavelet estimators
Felix Abramovich, Claudia Angelini, Daniela Canditiis
Bayes Factor, Bayes model, Bayesian paradox, Besov spaces, Minimax rates, Nonparametric regression, Point estimation, Posterior mean, Posterior median, Wavelets,