New approaches for choosing the ridge parameters

J. AL-JARARHA

Makale detayları

New approaches for choosing the ridge parameters

Yazarlar:

J. AL-JARARHA

Yayıncı:

Hacettepe University

Ana Başlıklar:

Analiz

Dergi:

Hacettepe Journal of Mathematics and Statistics 2018 Vol.47 Issue 6, pp.1625-1633

Belge Tipi:

Makale

Yayın Tarihi:

12/2018

Belge Dili:

İngilizce

Document ID (Org No.):

2000451741

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

Özet:

 

Consider the standard multiple linear regression model y=xβ+ε.y=xβ+ε.y=x\beta+\varepsilon. If the correlation matrix xtxxtxx^tx  is ill-conditioned, the ordinary least squared estimate (ols) ^ββ^\hat{\beta} of ββ\beta is not the best choice. In this paper, multiple regularization  parameters for different coefficients in ridge regression are proposed. The Mean Squared Error (MSE) of a ridge estimate  based on the multiple regularization parameters is less than or equal to the MSE of the ridge estimate based on Hoerl and Kennard, 1970. The proposed approach, depending onthe condition numbers, leave's zero for the largest eigenvalue of xtxxtxx^tx and gives the largest value  for the smallest eigenvalue of xtx.xtx.x^tx.Furthermore, if xtxxtxx^tx is nearly a unit matrix, xtxxtxx^tx  is not an ill-conditioned one. The proposed approach gives approximately the same results as the ols estimates. The proposed approach can also be modified to give other new ridge parameters. The modified approach depends on the eigenvalues of  xtxxtxx^tx and  differ from the ridge parameter proposed by Khalaf and Shukur by a factor. The body fat data set has severe multicollinearity and is used to compare different approaches.

Makale detayları

New approaches for choosing the ridge parameters

Yazarlar: J. AL-JARARHA

Yayıncı: Hacettepe University

Ana Başlıklar: Analiz

Dergi: Hacettepe Journal of Mathematics and Statistics 2018 Vol.47 Issue 6, pp.1625-1633

Belge Tipi: Makale

Yayın Tarihi: 12/2018

Belge Dili: İngilizce

Document ID (Org No.): 2000451741

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

J. AL-JARARHA

Yayıncı:

Hacettepe University

Ana Başlıklar:

Analiz

Dergi:

Hacettepe Journal of Mathematics and Statistics 2018 Vol.47 Issue 6, pp.1625-1633

Belge Tipi:

Makale

Yayın Tarihi:

12/2018

Belge Dili:

İngilizce

Document ID (Org No.):

2000451741

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X