A robust estimation method of location and scale with application in monitoring process variability

This thesis consists of two parts; theoretical and application. The first part proposes the development of a new method for robust estimation of location and scale, in data concentration step (C-step), of the most widely used method known as fast minimum covariance determinant (FMCD). This new me...

Full description

Saved in:

Bibliographic Details
Main Author:	Mohd Salleh, Rohayu
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://eprints.uthm.edu.my/1764/1/24p%20ROHAYU%20MOHD%20SALLEH.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-uthm-ep.1764
record_format	uketd_dc
spelling	my-uthm-ep.17642021-10-11T01:12:39Z A robust estimation method of location and scale with application in monitoring process variability 2013-08 Mohd Salleh, Rohayu QA Mathematics QA273-280 Probabilities. Mathematical statistics This thesis consists of two parts; theoretical and application. The first part proposes the development of a new method for robust estimation of location and scale, in data concentration step (C-step), of the most widely used method known as fast minimum covariance determinant (FMCD). This new method is as effective as FMCD and minimum vector variance (MVV) but with lower computational complexity. In FMCD, the optimality criterion of C-step is still quite cumbersome if the number of variables p is large because of the computation of sample generalized variance. This is the reason why MVV has been introduced. The computational complexity of the C-step in FMCD is of order ( ) 3 O p while MVV is ( ) 2 O p . This is a significant improvement especially for the case when p is large. In this case, although MVV is faster than FMCD, it is still time consuming. Thus, this is the principal motivation of this thesis, that is, to find another optimal criterion which is of far higher computational efficiency. In this study, two other different optimal criteria which will be able to reduce the running time of C-step is proposed. These criteria are (i) the covariance matrix equality and (ii) index set equality. Both criteria do not require any statistical computations, including the generalized variance in FMCD and vector variance in MVV. Since only a logical test is needed, the computational complexities of the C-step are of order ( ) ln O p p. The second part is the application of the proposed criteria in robust Phase I operation of multivariate process variability based on individual observations. Besides that, to construct a more sensitive Phase II operation, both Wilks’ W statistic and Djauhari’s F statistic are used. Both statistics have different distributions and is used to measure the effect of an additional observation on covariance structure. 2013-08 Thesis http://eprints.uthm.edu.my/1764/ http://eprints.uthm.edu.my/1764/1/24p%20ROHAYU%20MOHD%20SALLEH.pdf text en public phd doctoral Universiti Teknologi Malaysia Fakulti Sains
institution	Universiti Tun Hussein Onn Malaysia
collection	UTHM Institutional Repository
language	English
topic	QA Mathematics QA Mathematics
spellingShingle	QA Mathematics QA Mathematics Mohd Salleh, Rohayu A robust estimation method of location and scale with application in monitoring process variability
description	This thesis consists of two parts; theoretical and application. The first part proposes the development of a new method for robust estimation of location and scale, in data concentration step (C-step), of the most widely used method known as fast minimum covariance determinant (FMCD). This new method is as effective as FMCD and minimum vector variance (MVV) but with lower computational complexity. In FMCD, the optimality criterion of C-step is still quite cumbersome if the number of variables p is large because of the computation of sample generalized variance. This is the reason why MVV has been introduced. The computational complexity of the C-step in FMCD is of order ( ) 3 O p while MVV is ( ) 2 O p . This is a significant improvement especially for the case when p is large. In this case, although MVV is faster than FMCD, it is still time consuming. Thus, this is the principal motivation of this thesis, that is, to find another optimal criterion which is of far higher computational efficiency. In this study, two other different optimal criteria which will be able to reduce the running time of C-step is proposed. These criteria are (i) the covariance matrix equality and (ii) index set equality. Both criteria do not require any statistical computations, including the generalized variance in FMCD and vector variance in MVV. Since only a logical test is needed, the computational complexities of the C-step are of order ( ) ln O p p. The second part is the application of the proposed criteria in robust Phase I operation of multivariate process variability based on individual observations. Besides that, to construct a more sensitive Phase II operation, both Wilks’ W statistic and Djauhari’s F statistic are used. Both statistics have different distributions and is used to measure the effect of an additional observation on covariance structure.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohd Salleh, Rohayu
author_facet	Mohd Salleh, Rohayu
author_sort	Mohd Salleh, Rohayu
title	A robust estimation method of location and scale with application in monitoring process variability
title_short	A robust estimation method of location and scale with application in monitoring process variability
title_full	A robust estimation method of location and scale with application in monitoring process variability
title_fullStr	A robust estimation method of location and scale with application in monitoring process variability
title_full_unstemmed	A robust estimation method of location and scale with application in monitoring process variability
title_sort	robust estimation method of location and scale with application in monitoring process variability
granting_institution	Universiti Teknologi Malaysia
granting_department	Fakulti Sains
publishDate	2013
url	http://eprints.uthm.edu.my/1764/1/24p%20ROHAYU%20MOHD%20SALLEH.pdf
_version_	1747830863534489600

A robust estimation method of location and scale with application in monitoring process variability

Similar Items