Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models

Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models

Dalam bidang pemodelan regresi linear, regresi kuasa dua terkecil (LS) klasik adalah mudah dipengaruhi oleh titik terpencil manakala penganggar regresi rendah-kerosakan seperti regresi M dan regresi pengaruh terbatas mampu menahan pengaruh peratusan kecil titik terpencil. Penganggar tinggi-kerosa...

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Main Author: Alih, Ekele
Format: Thesis
Language:English
Published: 2015
Subjects:
QA1 Mathematics (General)
Online Access:http://eprints.usm.my/32288/
http://eprints.usm.my/32288/1/EKELE_ALIH.pdf
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author Alih, Ekele
author_facet Alih, Ekele
author_sort Alih, Ekele
building USM Institutional Repository
collection Online Access
description Dalam bidang pemodelan regresi linear, regresi kuasa dua terkecil (LS) klasik adalah mudah dipengaruhi oleh titik terpencil manakala penganggar regresi rendah-kerosakan seperti regresi M dan regresi pengaruh terbatas mampu menahan pengaruh peratusan kecil titik terpencil. Penganggar tinggi-kerosakan seperti kuasa dua trim terkecil (LTS) dan penganggar regresi (MM) adalah teguh terhadap sebanyak 50% daripada pencemaran data. Masalah prosedur penganggar ini termasuklah permintaan pengkomputeran luas dan kebolehubahan subpensampelan, kerentanan koefisien teruk terhadap kebolehubahan kecil dalam nilai awal, sisihan dalaman daripada trend umum dan kebolehan dalam data bersih dan situasi rendah-kerosakan. Kajian ini mencadangkan suatu penganggar regresi baru yang menyelesaikan masalah dalam model regresi berganda dan regresi multivariat serta menyediakan maklumat berguna tentang kehadiran dan struktur titik terpencil multivariat. In the field of linear regression modelling, the classical least squares (LS) regression is susceptible to a single outlier whereas low-breakdown regression estimators like M regression and bounded influence regression are able to resist the influence of a small percentage of outliers. High-breakdown estimators like the least trimmed squares (LTS) and MM regression estimators are resistant to as much as 50% of data contamination. The problems with these estimation procedures include enormous computational demands and subsampling variability, severe coefficient susceptibility to very small variability in initial values, internal deviation from the general trend and capabilities in clean data and in low breakdown situations. This study proposes a new high breakdown regression estimator that addresses these problems in multiple regression and multivariate regression models as well as providing insightful information about the presence and structure of multivariate outliers.
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format Thesis
id usm-32288
institution Universiti Sains Malaysia
institution_category Local University
language English
last_indexed 2025-11-15T17:04:57Z
publishDate 2015
recordtype eprints
repository_type Digital Repository
spelling usm-322882019-04-12T05:25:43Z http://eprints.usm.my/32288/ Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models Alih, Ekele QA1 Mathematics (General) Dalam bidang pemodelan regresi linear, regresi kuasa dua terkecil (LS) klasik adalah mudah dipengaruhi oleh titik terpencil manakala penganggar regresi rendah-kerosakan seperti regresi M dan regresi pengaruh terbatas mampu menahan pengaruh peratusan kecil titik terpencil. Penganggar tinggi-kerosakan seperti kuasa dua trim terkecil (LTS) dan penganggar regresi (MM) adalah teguh terhadap sebanyak 50% daripada pencemaran data. Masalah prosedur penganggar ini termasuklah permintaan pengkomputeran luas dan kebolehubahan subpensampelan, kerentanan koefisien teruk terhadap kebolehubahan kecil dalam nilai awal, sisihan dalaman daripada trend umum dan kebolehan dalam data bersih dan situasi rendah-kerosakan. Kajian ini mencadangkan suatu penganggar regresi baru yang menyelesaikan masalah dalam model regresi berganda dan regresi multivariat serta menyediakan maklumat berguna tentang kehadiran dan struktur titik terpencil multivariat. In the field of linear regression modelling, the classical least squares (LS) regression is susceptible to a single outlier whereas low-breakdown regression estimators like M regression and bounded influence regression are able to resist the influence of a small percentage of outliers. High-breakdown estimators like the least trimmed squares (LTS) and MM regression estimators are resistant to as much as 50% of data contamination. The problems with these estimation procedures include enormous computational demands and subsampling variability, severe coefficient susceptibility to very small variability in initial values, internal deviation from the general trend and capabilities in clean data and in low breakdown situations. This study proposes a new high breakdown regression estimator that addresses these problems in multiple regression and multivariate regression models as well as providing insightful information about the presence and structure of multivariate outliers. 2015-06 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/32288/1/EKELE_ALIH.pdf Alih, Ekele (2015) Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models. PhD thesis, Universiti Sains Malaysia.
spellingShingle QA1 Mathematics (General)
Alih, Ekele
Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models
title Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models
title_full Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models
title_fullStr Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models
title_full_unstemmed Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models
title_short Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models
title_sort cluster-based estimators for multiple and multivariate linear regression models
topic QA1 Mathematics (General)
url http://eprints.usm.my/32288/
http://eprints.usm.my/32288/1/EKELE_ALIH.pdf

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