On non-asymptotic bounds for estimation in generalized linear models with highly correlated design

Mathematics – Statistics Theory

Scientific paper

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Published at http://dx.doi.org/10.1214/074921707000000319 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000319

We study a high-dimensional generalized linear model and penalized empirical
risk minimization with $\ell_1$ penalty. Our aim is to provide a non-trivial
illustration that non-asymptotic bounds for the estimator can be obtained
without relying on the chaining technique and/or the peeling device.

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