×

Combining unbiased ridge and principal component regression estimators. (English) Zbl 1170.62047

Summary: In the presence of the multicollinearity problem, ordinary least squares (OLS) estimation is inadequate. To circumvent this problem, two well-known estimation procedures often suggested are the unbiased ridge regression (URR) estimator given by R. H. Crouse et al. [ibid. 24, No. 9, 2341–2354 (1995; Zbl 0937.62616)] and the \((r, k)\) class estimator given by M. Baye and D. Parker [ibid. 13, No. 2, 197–202 (1984)]. We propose a new class of estimators, namely modified \((r, k)\) class ridge regression (MCRR), which includes the OLS, the URR, the \((r, k)\) class, and the principal components regression (PCR) estimators. It is based on a criterion that combines the ideas underlying the URR and the PCR estimators. The standard properties of this new class estimator have been investigated and a numerical illustration is done. The conditions under which the MCRR estimator is better than the other two estimators have been investigated.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62H25 Factor analysis and principal components; correspondence analysis
62J05 Linear regression; mixed models

Citations:

Zbl 0937.62616
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Batah F., Far East J. Theoret. Statist. 24 pp 157– (2008)
[2] Batah F., Model Assisted Statist. Applic. 3 3 pp 201– (2008)
[3] DOI: 10.1080/03610928408828675
[4] DOI: 10.1080/03610929508831620 · Zbl 0937.62616
[5] Farebrother R., J. Roy. Statist. Soc. B. 38 pp 248– (1976)
[6] DOI: 10.2307/2286229 · Zbl 0369.62070
[7] DOI: 10.2307/1267351 · Zbl 0202.17205
[8] Hoerl A., Am. J. Math. Manag. Sci. 1 pp 583– (1981)
[9] DOI: 10.1080/03610927508827232 · Zbl 0296.62062
[10] DOI: 10.2307/1267205 · Zbl 0205.46102
[11] DOI: 10.2307/2283149
[12] DOI: 10.2307/1266855 · Zbl 0265.62017
[13] DOI: 10.1080/03610920601033652 · Zbl 1315.62062
[14] DOI: 10.1080/03610928708829583 · Zbl 0651.62068
[15] Rao C., Linear Models: Least Squares and Alternatives (1995) · Zbl 0846.62049
[16] Sarkar N., Statist. Probab. Lett. 21 pp 1987– (1996)
[17] DOI: 10.1080/03610927608827423 · Zbl 0342.62035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.