Topics in spline smoothing /
A new efficient O(n) algorithm is developed to compute smoothing spline estimators through use of the Kalman filter. The practical implementation of this algorithm requires only an understanding of basic programming. Various extensions of the smoothing spline estimator and computing algorithm are al...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
2001.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=725921591&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | A new efficient O(n) algorithm is developed to compute smoothing spline estimators through use of the Kalman filter. The practical implementation of this algorithm requires only an understanding of basic programming. Various extensions of the smoothing spline estimator and computing algorithm are also considered. In addition, this algorithm allows for the practical development of methods for adaptive selection of both the order of smoothing and the smoothing parameter. Simulation experiments are presented that show that adaptive order selection can improve estimator efficiency over the use of cubic smoothing splines. The smoothing spline boundary bias problem is solved through an application of the Eubank/Speckman (1991) Bias Reduction Theorem. An efficient O(n) algorithm is designed to compute this estimator. The special case of cubic smoothing spline boundary correction is investigated with application to the construction of confidence intervals. Precise analytic results are obtained for the linear boundary corrected smoothing spline and its associated risk properties. |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | ix, 77 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 74-76). |