Revıvıng some geometrıc aspects of shrınkage estımatıon ın lınear models
Yükleniyor...
Dosyalar
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
ANKARA UNIV, FAC SCI
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
It is well known that the least squares estimator is the best linear unbiased estimator of the parameter vector in a classical linear model. But, it is 'too long' as a vector and unreliable, confidence intervals are broad for some components especially in the case of multicollinearity. Shrinkage (contraction) type estimators are efficient remedial tools in order to solve problems caused by multicollinearity. In this study, we consider a class of componentwise shrunken estimators with typical members: Mayer and Willke's contraction estimator, Marquardt's principal component estimator, Hoerl and Kennard's ridge estimator, Liu's linear unified estimator and a discrete shrunken estimator. All estimators considered are "shorter" than the least squares estimator with respect to the Euclidean norm, biased, but insensitive to multicollinearity and admissible within the set of linear estimators with respect to unweighted squared error risk. Some behaviors of these estimators are illustrated geometrically by tracing their trajectories as functions of shrinkage factors in a two-dimensional parameter space.
Açıklama
WOS: 000463698900093
Anahtar Kelimeler
Contraction Estimator, Liu Estimator, Principal Component Estimator, Ridge Regression
Kaynak
Communıcatıons Faculty of Scıences Unıversıty of Ankara-serıes a1 Mathematıcs and Statıstıcs
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
68
Sayı
1
