SHRINKAGE ESTIMATORS OF THE LOCATION PARAMETER FOR CERTAIN SPHERICALLY SYMMETRIC DISTRIBUTIONS

ANN COHEN BRANDWEIN^{1}, STEFAN RALESCU^{2} AND WILLIAM E. STRAWDERMAN^{3}

1Department of Statistics, Baruch College of the City University of New York,

Box 513, 17 Lexington Av., New York, NY 10010, U.S.A.

2Department of Mathematics, Queens College of the City University of New York,

65-30 Kissena Boulevard, Flushing, NY 11367, U.S.A. 3Department of Statistics, Hill Center, Busch Campus, Rutgers University, New Brunswick, NJ 08903, U.S.A.

(Received September 4, 1991; revised September 16, 1992)

Abstract. We consider estimation of a location vector for particular subclasses of spherically symmetric distributions in the presence of a known or unknown scale parameter. Specifically, for these spherically symmetric distributions we obtain slightly more general conditions and larger classes of estimators than Brandwein and Strawderman (1991, Ann. Statist., 19, 1639–1650) under which estimators of the form X + ag(X) dominate X for quadratic loss, concave functions of quadratic loss and general quadratic loss.

Key words and phrases: Spherical symmetry, quadratic loss, concave loss, location parameter, unknown scale.