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The not-so-smoother Eveson, Jennifer Paige
Abstract
In this thesis, a local smoothing method, termed the not-so-smoother, designed to estimate discontinuous regression functions is proposed. Local smoothing techniques estimate the regression function at a given point by finding the "best fit" through the observations within a fixed neighbourhood of the point. The "best fit" can be the best constant fit (which gives the moving average smoother), the best linear fit, the best kdegree polynomial fit, et cetera. The not-so-smoother finds the best local broken constant fit, a piecewise constant function with exactly one simple discontinuity. Unlike any of the traditional local smoothing methods, the not-so-smoother uses discontinuous local fits and, therefore, has the ability to preserve discontinuities in the function. Consistency of the not-so-smoother under general conditions is proven. Performance of the smoother on simulated data, both continuous and discontinuous, is demonstrated, and an application to a real data set of electric current recordings through an ion channel in a cell membrane is also shown. Variations of the not-so-smoother which can lead to improved performance in certain situations are investigated.
Item Metadata
Title |
The not-so-smoother
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1996
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Description |
In this thesis, a local smoothing method, termed the not-so-smoother, designed to estimate
discontinuous regression functions is proposed. Local smoothing techniques estimate
the regression function at a given point by finding the "best fit" through the
observations within a fixed neighbourhood of the point. The "best fit" can be the best
constant fit (which gives the moving average smoother), the best linear fit, the best kdegree
polynomial fit, et cetera. The not-so-smoother finds the best local broken constant
fit, a piecewise constant function with exactly one simple discontinuity. Unlike any of
the traditional local smoothing methods, the not-so-smoother uses discontinuous local
fits and, therefore, has the ability to preserve discontinuities in the function.
Consistency of the not-so-smoother under general conditions is proven. Performance
of the smoother on simulated data, both continuous and discontinuous, is demonstrated,
and an application to a real data set of electric current recordings through an ion channel
in a cell membrane is also shown. Variations of the not-so-smoother which can lead to
improved performance in certain situations are investigated.
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Extent |
2824789 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-02-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0087254
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1996-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.