ON A MULTIPARAMETER VERSION OF TUKEY’S LINEAR SENSITIVITY MEASURE AND ITS PROPERTIES

B. CHANDRASEKAR^{1} AND N. BALAKRISHNAN^{2}

1Department of Statistics, Loyola College, Chennai– 600 034, Tamilnadu, India 2Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

(Received May 29, 2001; revised December 13, 2001)

Abstract. A multiparameter version of Tukey’s (1965, Proc. Nat. Acad. Sci. U.S.A., 53, 127–134) linear sensitivity measure, as a measure of informativeness in the joint distribution of a given set of random variables, is proposed. The proposed sensitivity measure, under some conditions, is a matrix which is non-negative definite, weakly additive, monotone and convex. Its relation to Fisher information matrix and the best linear unbiased estimator (BLUE) are investigated. The results are applied to the location-scale model and it is observed that the dispersion matrix of the BLUE of the vector location-scale parameter is the inverse of the sensitivity measure. A similar property was established by Nagaraja (1994, Ann. Inst. Statist. Math., 46, 757–768) for the single parameter case when applied to the location and scale models. Two illustrative examples are included.

Key words and phrases: BLUE, Fisher information, location-scale model, multiparameter, sensitivity measure.