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   -> Volume 6, Issue 1


Thesis: A Statistical wavelet approach to model selection
 
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Geung-Hee Lee (ghlee@picard.tamu.edu)
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PostPosted: Tue Dec 24, 1996 6:50 pm    
Subject: Thesis: A Statistical wavelet approach to model selection
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#8 Thesis: A Statistical wavelet approach to model selection

My Ph.D. thesis, entitled:

"A Statistical wavelet approach to model selection and data driven
Neyman smooth tests."

It can be obtained by anonymous ftp to

ftp://stat.tamu.edu/pub/aliaw/disset.ps.gz.

ABSTRACT

Wavelets have received a lot of attention in statistics
since Donoho and Johnstone(1994, Biometrika) introduced wavelet shrinkage
estimators, which include two important ideas -- wavelets as a new local
basis and thresholding. From these ideas, we can reilluminate the previous
methods based on Fourier series and truncated estimators.
In this dissertation, we develop model selection criteria in
the orthogonal series estimator and
data driven Neyman smooth tests as lack-of-fit tests using these two ideas.

Regression analysis can be explained as an iterative cycling procedure
between model selection and lack-of-fit testing of the selected model.
We develop new model selection criteria to detect low as well as
dominant high frequency behavior for a truncated series estimator. For
the wavelet series estimator, we propose a rule to choose a threshold
and a truncation point simultaneously. This estimator is shown to
provide better performance in terms of visual quality and mean square
error compared with wavelet series estimators with fixed truncation
points such as $RiskShrink$ and $VisuShrink$.

Data driven Neyman smooth tests are used as omnibus tests to detect
misspecification error of the model. The performance of data driven
Neyman smooth tests depends on the selected smoothing parameter, basis
and the form of orthogonal series estimator. In this dissertation, we
modify the data driven Neyman smooth test in order to improve its
performance for a wider class of alternatives using different model
selection criteria, different bases such as wavelets, and different
estimators.

GeungHee Lee.
Statistics, Texas A&M
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