## 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

Zbl 0937.62616
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### References:

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