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Soumen Lahiri -Texas A & M University

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”Rates of convergence of the Adaptive LASSO estimators to the Oracle distribution and higher order refinements by the bootstrap”
29 November 2012 from 4:00 PM to 5:00 PM
111 Tyson Bldg.
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Zou ( 2006; J. Amer.  Statist.  Assoc.,) proposed the ALASSO method for simultaneous variable selection and estimation of the non-zero regression parameters, and established its oracle property. In this paper, we provide a precise description of the rate of convergence of the ALASSO estimators of the non-zero components to the oracle distribution.  It is shown that the rate critically depends on the choices of the  penalty  parameter and the  initial  estimator,  and that  confidence intervals (CIs) based on the oracle limit  law have poor coverage accuracy. As an alternative, we consider the  residual  bootstrap method for the ALASSO estimators  and  show that a naive application of the bootstrap, although consistent, may result in a very slow rate of approximation, with or without studentization. We construct a suitably bias-adjusted and studentized pivotal version of the ALASSO estimator and show that the bootstrap applied to this modified pivot achieves second-order correctness, even when the dimension of the non-zero regression parameters is unbounded. Results from a moderately large simulation study show marked improvement in coverage accuracy for the bootstrap CIs over the oracle based CIs in finite samples.


* Joint work with Arindam Chatterjee, ISI, Delhi.

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