398 citations · 762 across the 5 of their papers we have counts for
4 papers · 1 filter
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…
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…
Local polynomial regression on unknown manifolds
Peter J. Bickel, Bo Li
We reveal the phenomenon that ``naive'' multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal con…