Lp norm estimation procedures and an L1 norm algorithm for unconstrained and constrained estimation for linear models
| dc.contributor.author | Kim, Buyong | en |
| dc.contributor.committeechair | Skarpness, Bradley O. | en |
| dc.contributor.committeemember | Foutz, Robert | en |
| dc.contributor.committeemember | Reynolds, Marion R. Jr. | en |
| dc.contributor.committeemember | Krutchkoff, Richard G. | en |
| dc.contributor.committeemember | Sherali, Hanif D. | en |
| dc.contributor.department | Statistics | en |
| dc.date.accessioned | 2015-06-24T13:35:24Z | en |
| dc.date.available | 2015-06-24T13:35:24Z | en |
| dc.date.issued | 1986 | en |
| dc.description.abstract | When the distribution of the errors in a linear regression model departs from normality, the method of least squares seems to yield relatively poor estimates of the coefficients. One alternative approach to least squares which has received a great deal of attention of late is minimum L<sub>p</sub> norm estimation. However, the statistical efüciency of a L<sub>p</sub> estimator depends greatly on the underlying distribution of errors and on the value of p. Thus, the choice of an appropriate value of p is crucial to the effectiveness of <sub>p</sub> estimation. Previous work has shown that L₁ estimation is a robust procedure in the sense that it leads to an estimator which has greater statistical efficiency than the least squares estimator in the presence of outliers, and that L₁ estimators have some- desirable statistical properties asymptotically. This dissertation is mainly concerned with the development of a new algorithm for L₁ estimation and constrained L₁ estimation. The mainstream of computational procedures for L₁ estimation has been the simplex-type algorithms via the linear programming formulation. Other procedures are the reweighted least squares method, and. nonlinear programming technique using the penalty function approach or descent method. A new computational algorithm is proposed which combines the reweighted least squares method and the linear programming approach. We employ a modified Karmarkar algorithm to solve the linear programming problem instead of the simplex method. We prove that the proposed algorithm converges in a finite number of iterations. From our simulation study we demonstrate that our algorithm requires fewer iterations to solve standard problems than are required by the simplex-type methods although the amount of computation per iteration is greater for the proposed algorithm. The proposed algorithm for unconstrained L₁ estimation is extended to the case where the L₁ estimates of the parameters of a linear model satisfy certain linear equality and/or inequality constraints. These two procedures are computationally simple to implement since a weighted least squares scheme is adopted at each iteration. Our results indicate that the proposed L₁ estimation procedure yields very accurate and stable estimates and is efficient even when the problem size is large. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | ix, 133 leaves | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/53627 | en |
| dc.language.iso | en_US | en |
| dc.publisher | Virginia Polytechnic Institute and State University | en |
| dc.relation.isformatof | OCLC# 15280160 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1986.K57 | en |
| dc.subject.lcsh | Linear models (Statistics) | en |
| dc.title | Lp norm estimation procedures and an L1 norm algorithm for unconstrained and constrained estimation for linear models | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Statistics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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