Type of Document	Dissertation
Author	Gupta, Shuva
URN	etd-05092009-002445
Title	A Study Of The Asymptotic Properties Of Lasso Estimates For Correlated Data
Degree	Doctor of Philosophy
Department	Statistics, Department of
Advisory Committee	Advisor Name Title Florentina Bunea Committee Chair Marten Wegkamp Committee Member Myles Hollander Committee Member Joshua Gert Outside Committee Member
Keywords	Lasso Correlated Data Asymptotic
Date of Defense	2009-05-01
Availability	unrestricted
Abstract In this thesis we investigate post-model selection properties of L1 penalized weighted least squares estimators in regression models with a large number of variables M and correlated errors. We focus on correct subset selection and on the asymptotic distribution of the penalized estimators. In the simple case of AR(1) errors we give conditions under which correct subset selection can be achieved via our procedure. We then provide a detailed generalization of this result to models with errors that have a weak-dependency structure (Doukhan 1996). In all cases, the number M of regression variables is allowed to exceed the sample size n. We further investigate the asymptotic distribution of our estimates, when M < n, and show that under appropriate choices of the tuning parameters the limiting distribution is multivariate normal. This generalizes to the case of correlated errors the result of Knight and Fu (2000), obtained for regression models with independent errors.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Gupta_S_Dissertation_2009r.pdf 504.01 Kb 00:02:20 00:01:12 00:01:03 00:00:31 00:00:02