Outlier detection methods of unreplicated linear functional relationship model for circular variables

This study is on modelling circular data and proposed several methods of detecting outliers of the model considered in the study. In particular, the linear functional relationship model is considered where the maximum likelihood parameters and the covariance matrix are derived for the case where the...

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Main Author:	Nurkhairany Amyra, Mokhtar
Format:	Thesis
Language:	English English
Published:	2019
Subjects:	HA Statistics
Online Access:	http://ir.upnm.edu.my/id/eprint/184/1/OUTLIER%20DETECTION%20METHODS%20%2825p%29.pdf http://ir.upnm.edu.my/id/eprint/184/2/OUTLIER%20DETECTION%20METHODS%20%28Full%29.pdf
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spelling	my-upnm-ir.1842023-03-30T01:52:02Z Outlier detection methods of unreplicated linear functional relationship model for circular variables 2019-07-02 Nurkhairany Amyra, Mokhtar HA Statistics This study is on modelling circular data and proposed several methods of detecting outliers of the model considered in the study. In particular, the linear functional relationship model is considered where the maximum likelihood parameters and the covariance matrix are derived for the case where the error concentration parameters are unequal since previous study only considered the parameter estimation for the case of equal error concentration. The parameter estimate of x variable is improved by applying the iterative procedure in which the incidental parameter stops accumulating after the values converge to a finite number. The parameter estimate of the concentration parameter is estimated by using modified Bessel function in which it is expanded to become a cubic function. Monte Carlo simulation study shows that the proposed parameter estimations give a small bias with mean resultant length near to 1 and small estimated root meansquare errors that indicate an adequacy of the estimation. Next, some methods to detect the presence of outlier in circular data are discussed. Previous studies only considered outlier detection methods for equal error concentration case. Therefore, in this thesis, all outlier detection methods take into account of both equal and unequal error concentration parameters in the model. The first proposed method in outlier detection is by using the determinantal equation of the covariance matrix, called covratio, in which the covariance matrix is based on the one derived in the first part of the study. Another two proposed methods used to detect the outlier are by using the difference mean circular errors. The two trigonometric functions are the cosine (FDMCEC) and sine (FDMCES) functions. The cut-off equations are derived based on the 5% upper percentile of the simulation study for each method for 95% confident level. The feasibility of all of the methods is assessed by the power of performance in Monte Carlo simulation studies when outlier is planted in the data. The results from the simulation study suggest that the power of performance for all three outlier detection methods achieves the maximum percentage which is 100% as the level of contamination increases. Hence, this suggests the feasibility of the method used in outlier detection. 2019-07 Thesis http://ir.upnm.edu.my/id/eprint/184/ http://ir.upnm.edu.my/id/eprint/184/1/OUTLIER%20DETECTION%20METHODS%20%2825p%29.pdf text en public http://ir.upnm.edu.my/id/eprint/184/2/OUTLIER%20DETECTION%20METHODS%20%28Full%29.pdf text en validuser phd doctoral Universiti Pertahanan Nasional Malaysia Centre For Graduate Studies
institution	Universiti Pertahanan Nasional Malaysia
collection	UPNM Institutional Repository
language	English English
topic	HA Statistics
spellingShingle	HA Statistics Nurkhairany Amyra, Mokhtar Outlier detection methods of unreplicated linear functional relationship model for circular variables
description	This study is on modelling circular data and proposed several methods of detecting outliers of the model considered in the study. In particular, the linear functional relationship model is considered where the maximum likelihood parameters and the covariance matrix are derived for the case where the error concentration parameters are unequal since previous study only considered the parameter estimation for the case of equal error concentration. The parameter estimate of x variable is improved by applying the iterative procedure in which the incidental parameter stops accumulating after the values converge to a finite number. The parameter estimate of the concentration parameter is estimated by using modified Bessel function in which it is expanded to become a cubic function. Monte Carlo simulation study shows that the proposed parameter estimations give a small bias with mean resultant length near to 1 and small estimated root meansquare errors that indicate an adequacy of the estimation. Next, some methods to detect the presence of outlier in circular data are discussed. Previous studies only considered outlier detection methods for equal error concentration case. Therefore, in this thesis, all outlier detection methods take into account of both equal and unequal error concentration parameters in the model. The first proposed method in outlier detection is by using the determinantal equation of the covariance matrix, called covratio, in which the covariance matrix is based on the one derived in the first part of the study. Another two proposed methods used to detect the outlier are by using the difference mean circular errors. The two trigonometric functions are the cosine (FDMCEC) and sine (FDMCES) functions. The cut-off equations are derived based on the 5% upper percentile of the simulation study for each method for 95% confident level. The feasibility of all of the methods is assessed by the power of performance in Monte Carlo simulation studies when outlier is planted in the data. The results from the simulation study suggest that the power of performance for all three outlier detection methods achieves the maximum percentage which is 100% as the level of contamination increases. Hence, this suggests the feasibility of the method used in outlier detection.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Nurkhairany Amyra, Mokhtar
author_facet	Nurkhairany Amyra, Mokhtar
author_sort	Nurkhairany Amyra, Mokhtar
title	Outlier detection methods of unreplicated linear functional relationship model for circular variables
title_short	Outlier detection methods of unreplicated linear functional relationship model for circular variables
title_full	Outlier detection methods of unreplicated linear functional relationship model for circular variables
title_fullStr	Outlier detection methods of unreplicated linear functional relationship model for circular variables
title_full_unstemmed	Outlier detection methods of unreplicated linear functional relationship model for circular variables
title_sort	outlier detection methods of unreplicated linear functional relationship model for circular variables
granting_institution	Universiti Pertahanan Nasional Malaysia
granting_department	Centre For Graduate Studies
publishDate	2019
url	http://ir.upnm.edu.my/id/eprint/184/1/OUTLIER%20DETECTION%20METHODS%20%2825p%29.pdf http://ir.upnm.edu.my/id/eprint/184/2/OUTLIER%20DETECTION%20METHODS%20%28Full%29.pdf
_version_	1813223573011038208

Outlier detection methods of unreplicated linear functional relationship model for circular variables

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