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Study of the Asymptotic Properties of Lasso Estimates for Correlated Data

Title: A Study of the Asymptotic Properties of Lasso Estimates for Correlated Data.
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Name(s): Gupta, Shuva, 1979-, author
Bunea, Florentina, professor directing dissertation
Gert, Joshua, outside committee member
Hollander, Myles, committee member
Wegkamp, Marten, committee member
Department of Statistics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2009
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: 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.
Identifier: FSU_migr_etd-3896 (IID)
Submitted Note: A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2009.
Date of Defense: May 1, 2009.
Keywords: Lasso, Correlated Data, Asymptotic
Bibliography Note: Includes bibliographical references.
Advisory Committee: Florentina Bunea, Professor Directing Dissertation; Joshua Gert, Outside Committee Member; Myles Hollander, Committee Member; Marten Wegkamp, Committee Member.
Subject(s): Statistics
Probabilities
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-3896
Owner Institution: FSU

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Gupta, S. (2009). A Study of the Asymptotic Properties of Lasso Estimates for Correlated Data. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-3896