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Ulrike Schneider, Göttingen Print
Friday, 05 November 2010, 14:30 - 15:30

On Distributional Properties of Penalized Maximum Likelihood Estimators

Ulrike Schneider, University of Göttingen

Abstract: Penalized least squares (or maximum likelihood) estimators, such as the famous Lasso estimator, have been studied intensively in the last few years. While many properties of these estimators are now well understood, the understanding of their distributional characteristics, such as finite-sample and large-sample limit distributions, risk properties and confidence sets, is still incomplete.

We study the distribution of several of these estimators, such as the Lasso, the adaptive Lasso and the hard-thresholding estimator within a normal orthogonal linear regression model. We derive finite-sample as well as large-sample limit distributions and demonstrate that these distributions are typically highly non-normal. Uniform convergence rates are obtained and shown to be slower than $n^{-1/2}$ in case the estimator is sparse, i.e. tuned to perform consistent model selection. We also calculate the risk of these estimators, derive honest confidence intervals, and discuss extensions to the non-orthogonal case. Finally, we provide an impossibility result regarding the estimability of the distribution function.

Location: 2NOP salle des profs - Plaine
Contact: Jacqueline Bottemanne, This e-mail address is being protected from spam bots, you need JavaScript enabled to view it

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