A data-driven smoothing parameter selection for robust nonparametric regression /
Nonparametric regression methodology provides flexible tools
| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1995.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=742164431&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Nonparametric regression methodology provides flexible tools for analyzing unknown regression relationships. In the application of nonparametric methods, it is crucial to select a proper smoothing or bandwidth parameter which controls the smoothness of the resulting function estimate. This dissertation presents a procedure to estimate the optimal bandwidth for bivariate local linear regression when the data are contaminated by a heavy-tailed error distribution. First, a method for robust estimation of a bivariate regression function is proposed, and the asymptotic properties of the estimator are derived. Second, an asymptotically efficient bandwidth selection rule, the "plug-in" method, is proposed to estimate the optimal bandwidths from the data. Third, a nonparametric estimator of residual variance is proposed. It basically is an application of local least squares regression. A minor modification to robustify the variance estimate is also discussed. These methods are demonstrated and evaluated through various simulation studies. It is found that the "plug-in" rule improves upon the cross- validation procedure in various ways: (1) better relative rate of convergence; (2) computational saving from not requiring numerical minimization; (3) reliably good performance for smooth regression surfaces in simulations. |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | viii, 76 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references. |