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. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of
Doctor of Philosophy. / Summer Semester, 2009. / May 1, 2009. / Lasso, Correlated Data, Asymptotic / Includes bibliographical references. / Florentina Bunea, Professor Directing Dissertation; Joshua Gert, Outside Committee Member; Myles Hollander, Committee Member; Marten Wegkamp, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_254257 |
| Contributors | Gupta, Shuva, 1979- (authoraut), 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) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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