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Smoothing parameter selection when errors are correlated and application to ozone data St-Aubin, Robert
Abstract
Automatic smoothing parameter selection methods for nonparametric regression like cross-validation and generalized cross-validation are known to be severely affected by dependence in the regression errors. We proposed, in this work, to modify some of the ideas used in the cross-validation criterion in kernel regression with dependent errors and apply them to smoothing splines with model based penalty. Model based penalty smoothing permits us to keep the flexibility of the nonparametric methods while it also allows us to specify a favoured parametric model which can help improve on the estimate of the regression function. We consider the "modified cross-validation" (also known as Leave—21+1 out) and the "blockwise cross-validation" smoothing parameter selection techniques which were initially proposed by Hardle and Vieu (1992) and Wehrly and Hart (1988) respectively. These two smoothing parameter selection techniques take correlation into account and alleviate its effect on the regression function estimation. We use a simulation study to evaluate the performance of our two smoothing parameter selection techniques. We compare the results with a few commonly used parametric techniques. Our techniques are also applied to an air pollution data set where we estimate the underlying trend of daily and monthly ground ozone levels in southern Ontario.
Item Metadata
Title |
Smoothing parameter selection when errors are correlated and application to ozone data
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1998
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Description |
Automatic smoothing parameter selection methods for nonparametric regression
like cross-validation and generalized cross-validation are known to be
severely affected by dependence in the regression errors. We proposed, in
this work, to modify some of the ideas used in the cross-validation criterion in
kernel regression with dependent errors and apply them to smoothing splines
with model based penalty. Model based penalty smoothing permits us to keep
the flexibility of the nonparametric methods while it also allows us to specify
a favoured parametric model which can help improve on the estimate of the
regression function.
We consider the "modified cross-validation" (also known as Leave—21+1
out) and the "blockwise cross-validation" smoothing parameter selection techniques
which were initially proposed by Hardle and Vieu (1992) and Wehrly
and Hart (1988) respectively. These two smoothing parameter selection techniques
take correlation into account and alleviate its effect on the regression
function estimation.
We use a simulation study to evaluate the performance of our two
smoothing parameter selection techniques. We compare the results with a few commonly used parametric techniques. Our techniques are also applied to
an air pollution data set where we estimate the underlying trend of daily and
monthly ground ozone levels in southern Ontario.
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Extent |
7771762 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-05-26
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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 |
10.14288/1.0088619
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1998-11
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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.