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Error variance estimation in nonparametric regression models

Alharbi, Yousef Fayz M (2013)
Ph.D. thesis, University of Birmingham.

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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.

Type of Work:Ph.D. thesis.
Supervisor(s):Patil, Prakash N.
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:4383
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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