Alih, Ekele
(2015)
Cluster-Based Estimators For
Multiple And Multivariate Linear
Regression Models.
PhD thesis, Universiti Sains Malaysia.
Abstract
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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