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The Dantzig selector:statistical estimation when p is much larger than n
Statistical linear model model selection ideal estimation oracle inequalities sparse solutions to underdetermined systems `1-minimization linear programming restricted orthonormality geometry in high dimensions random matrices
2015/6/17
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...
Modern statistical estimation via oracle inequalities
Modern statistical estimation oracle inequalities
2015/6/17
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...
REJOINDER: THE DANTZIG SELECTOR:STATISTICAL ESTIMATION WHEN P IS MUCH LARGER THAN N
DANTZIG SELECTOR STATISTICAL ESTIMATION MUCH LARGER THAN N
2015/6/17
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...
Supplementary materials for Statistical Estimation and Testing via the Sorted 1 Norm
Supplementary materials Statistical Estimation Sorted 1 Norm
2015/6/17
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...
Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence
Entropy estimation quadratic R′enyi entropy stationarym-dependent sequence inter-point distances U-statistics
2013/4/27
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...
Certain Relations between Mutual Information and Fidelity of Statistical Estimation
Certain Relations Mutual Information Fidelity of Statistical Estimation
2010/10/19
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 ...
Thresholded Lasso for high dimensional variable selection and statistical estimation
Linear regression Lasso Gauss-Dantzig Selector 1 regularization 0 penalty multiple-stepprocedure ideal model selection
2010/3/10
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 ...