# Thresholded Lasso for High Dimensional Variable Selection and Statistical Estimation *

@inproceedings{ZhouThresholdedLF,
title={Thresholded Lasso for High Dimensional Variable Selection and Statistical Estimation *},
author={Shuheng Zhou}
}
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 β ∈ R p in a linear model Y = Xβ + ǫ, where X n×p is a design matrix normalized to have column ℓ 2 norm √ n, and ǫ ∼ N (0, σ 2 I n). We show that under the restricted eigenvalue (RE) condition (Bickel-Ritov-Tsybakov 09), it is possible to achieve the ℓ 2 loss within a logarithmic factor of the… CONTINUE READING
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