Cluster-Based Estimators For Multiple And Multivariate Linear Regression Models - Alih, Ekele (2015)

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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.