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In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Xβ + z, where β ∈ Rp is...
A number of fundamental results in modern statistical theory involve thresholding estimators. This survey paper aims at reconstructing the history of how thresholding rules came to be popular in stati...
First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation. The comments all underlie the importance and timeliness of the to...
In this note we give a proof showing that even though the number of false discoveries and the total number of discoveries are not continuous functions of the parameters, the formulas we obtain for the...
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We cons...
I present several new relations between mutual information (MI) and statistical estimation error for a system that can be regarded simultaneously as a communication channel and as an estimator of an ...
Given n noisy samples with p dimensions, where n  p, we show that the multi-step thresholding procedure based on the Lasso – we call it the Thresholded Lasso, can accurately estimate a sparse vector ...

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