2.5k citations · 9k across the 50 of their papers we have counts for
6 papers · 2 filters
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…
Simultaneous analysis of Lasso and Dantzig selector
Peter J. Bickel, Ya'acov Ritov, Alexandre B. Tsybakov
We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the gener…