Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 3, 437--447

PREFERENCE REGIONS OF RIDGE REGRESSION AND OLS ACCORDING TO PITMAN'S CRITERION

By

ALESSANDRO BERTUZZI, ALBERTO GANDOLFI and CARMELA SINISGALLI Instituto di Analisi dei Sistemi ed Informatica del CNR, Roma

SUMMARY. For the multiple linear regression model, regions in the parameter space are constructed, in which the ridge estimator with a given value of the biasing parameter is preferred to the OLS estimator and, respectively, the OLS estimator is preferred to ridge estimator, according to the Pitman's criterion under quadratic loss. These regions are compared with the corresponding ones obtained according to the MSE criterion.

AMS (1991) subject classification. 62J05, 62J07.

Key words and phrases. Multiple linear regression; ridge regression; ordinary least squares; Pitman's measure of closeness.

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