Reviving some geometric aspects of shrinkage estimation in linear models

Fikri AKDENİZ; Fikri ÖZTÜRK

doi:https://doi.org/10.31801/cfsuasmas.508223

Makale detayları

Reviving some geometric aspects of shrinkage estimation in linear models

Yazarlar:

Fikri AKDENİZ | Fikri ÖZTÜRK

Yayıncı:

Ankara University

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2019 Vol.68 Issue 1, pp.1123-1143

Belge Tipi:

Makale

Yayın Tarihi:

1/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000909555

Sıklık:

Üç Aylık

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.31801/cfsuasmas.508223

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.

Makale detayları

Reviving some geometric aspects of shrinkage estimation in linear models

Yazarlar: Fikri AKDENİZ | Fikri ÖZTÜRK

Yayıncı: Ankara University

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2019 Vol.68 Issue 1, pp.1123-1143

Belge Tipi: Makale

Yayın Tarihi: 1/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000909555

Sıklık: Üç Aylık

eISSN: 2618-6470

pISSN: 1303-5991

DOI: https://doi.org/10.31801/cfsuasmas.508223

Sayı

Yazarlar:

Fikri AKDENİZ | Fikri ÖZTÜRK

Yayıncı:

Ankara University

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2019 Vol.68 Issue 1, pp.1123-1143

Belge Tipi:

Makale

Yayın Tarihi:

1/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000909555

Sıklık:

Üç Aylık

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.31801/cfsuasmas.508223