AISM 54, 796-805

© 2002 ISM

## On a multiparameter version of Tukey's linear sensitivity measure and its properties

### B. Chandrasekar^{1} and N. Balakrishnan^{2}

^{1}Department of Statistics, Loyola College, Chennai-
600 034, Tamilnadu, India

^{2}Department 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.

**Source**
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