2.5k citations · 9k across the 50 of their papers we have counts for
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Discussion of: Treelets--An adaptive multi-scale basis for sparse unordered data
Peter J. Bickel, Ya'acov Ritov
Discussion of "Treelets--An adaptive multi-scale basis for sparse unordered data" [arXiv:0707.0481]
Sharp failure rates for the bootstrap particle filter in high dimensions
Peter Bickel, Bo Li, Thomas Bengtsson
We prove that the maximum of the sample importance weights in a high-dimensional Gaussian particle filter converges to unity unless the ensemble size grows exponentially in the sys…
Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
Thomas Bengtsson, Peter Bickel, Bo Li
It has been widely realized that Monte Carlo methods (approximation via a sample ensemble) may fail in large scale systems. This work offers some theoretical insight into this phen…
Discussion: The Dantzig selector: Statistical estimation when is much larger than
Peter J. Bickel
Discussion of "The Dantzig selector: Statistical estimation when is much larger than " [math/0506081]
Regularized estimation of large covariance matrices
Peter J. Bickel, Elizaveta Levina
This paper considers estimating a covariance matrix of variables from observations by either banding or tapering the sample covariance matrix, or estimating a banded versio…
Hierarchical selection of variables in sparse high-dimensional regression
Peter J. Bickel, Ya'acov Ritov, Alexander B. Tsybakov
We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sp…