Functional data analysis is a eld in statistics that analyzes data which are dependent
on time or space and from which inference can be conducted. Functional data
analysis methods can estimate residuals from functional regression models that in
turn require robust univariate density estimators for error density estimation. The
accurate estimation of the error density from the residuals allows evaluation of the
performance of functional regression estimation. Kernel density estimation using
maximum likelihood cross-validation and Bayesian bandwidth selection techniques
with a Gaussian kernel are reproduced and compared to least-squares cross-validation
and plug-in bandwidth selection methods with an Epanechnikov kernel. For simulated
data, Bayesian bandwidth selection methods for kernel density estimation are
shown to give the minimum mean expected square error for estimating the error density,
but are computationally ine cient and may not be adequately robust for real
data. The (bounded) Epanechnikov kernel function is shown to give similar results as
the Gaussian kernel function for error density estimation after functional regression.
When the functional regression model is applied to a chemometric data set, the local
least-squares cross-validation method, used to select the bandwidth for the functional
regression estimator, is shown to give a signi cantly smaller mean square predicted
error than that obtained with Bayesian methods. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/16575 |
| Date | 06 1900 |
| Creators | Thompson, John R.J. |
| Contributors | Racine, Jeffrey S., Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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