Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 3, pp. 443--459

A NEW BIASED ESTIMATOR IN LINEAR REGRESSION AND A DETAILED ANALYSIS OF THE WIDELY-ANALYSED DATASET ON PORTLAND CEMENT

By

SELAHATTIN KAÇIRANLAR, SADULLAH SAKALLIOGLU, FIKRI AKDENIZ University of Çukurova, Adana, Turkey
GEORGE P. H. STYAN, McGill University, Montréeal, Québec, Canada

and

HANS JOACHIM WERNER, University of Bonn, Bonn, Germany

SUMMARY. This paper deals with the standard multiple linear regression model (y,Xb ,s2I), where the model matrix X is assumed to be of full column rank. We introduce a new biased estimator for b and discuss its properties in some detail. In particular, we show that our new estimator is superior, in the scalar mean-squared error sense, to both the usual restricted least-squares estimator and to the new biased estimator introduced by Liu (1993). We illustrate our findings with a numerical example based on the widely-analysed dataset on Portland cement, cf. Woods, Steinour and Starke (1932), Hald (1952, pp. 635--652), Piepel and Redgate (1998).

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

Key words and phrases. Anti-quirk; biased estimator; ill-conditioning; least squares estimator; Liu estimator; mean-squared error; multicollinearity; Portland cement data; quirk; restricted least squares; ridge regression estimator.

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