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Title: Error variance estimation in nonparametric regression models
Author: Alharbi, Yousef Fayz M.
ISNI:       0000 0004 2738 1990
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2013
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In this thesis, we take a fresh look at the error variance estimation in nonparametric regression models. The requirement for a suitable estimator of error variance in nonparametric regression models is well known and hence several estimators are suggested in the literature. We review these estimators and classify them into two types. Of these two types, one is difference-based estimators, whereas the other is obtained by smoothing the residual squares. We propose a new class of estimators which, in contrast to the existing estimators, is obtained by smoothing the product of residual and response variable. The properties of the new estimator are then studied in the settings of homoscedastic (variance is a constant) and heteroscedastic (variance is a function of x ) nonparametric regression models. In the current thesis, definitions of the new error variance estimators are provided in these two different settings. For these two proposed estimators, we carry out the mean square analysis and we then find their MSE-optimal bandwidth. We also study the asymptotic behaviour of the proposed estimators and we show that the asymptotic distributions in both settings are asymptotically normal distributions. We then conduct simulation studies to exhibit their finite sample performances.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics