The purpose of this study is to determine the effect of three improvement methods on nonparametric kernel
regression estimators. The improvement methods are applied to the Nadaraya-Watson estimator with crossvalidation
bandwidth selection, the Nadaraya-Watson estimator with plug-in bandwidth selection, the local
linear estimator with plug-in bandwidth selection and a bias corrected nonparametric estimator proposed by Yao
(2012). The di erent resulting regression estimates are evaluated by minimising a global discrepancy measure,
i.e. the mean integrated squared error (MISE).
In the machine learning context various improvement methods, in terms of the precision and accuracy of an
estimator, exist. The rst two improvement methods introduced in this study are bootstrapped based. Bagging
is an acronym for bootstrap aggregating and was introduced by Breiman (1996a) from a machine learning
viewpoint and by Swanepoel (1988, 1990) in a functional context. Bagging is primarily a variance reduction
tool, i.e. bagging is implemented to reduce the variance of an estimator and in this way improve the precision of
the estimation process. Bagging is performed by drawing repetitive bootstrap samples from the original sample
and generating multiple versions of an estimator. These replicates of the estimator are then used to obtain an
aggregated estimator. Bragging stands for bootstrap robust aggregating. A robust estimator is obtained by
using the sample median over the B bootstrap estimates instead of the sample mean as in bagging.
The third improvement method aims to reduce the bias component of the estimator and is referred to as boosting.
Boosting is a general method for improving the accuracy of any given learning algorithm. The method starts
of with a sensible estimator and improves iteratively, based on its performance on a training dataset.
Results and conclusions verifying existing literature are provided, as well as new results for the new methods. / MSc (Statistics), North-West University, Potchefstroom Campus, 2015
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/15345 |
| Date | January 2014 |
| Creators | Krugell, Marike |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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