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.


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


Zbl 0937.62616
Full Text: DOI


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