TUKEY’S LINEAR SENSITIVITY AND ORDER STATISTICS

H. N. NAGARAJA

Department of Statistics, The Ohio State University, 141 Cockins Hall, 1958 Neil Avenue, Columbus, OH 43210, U.S.A.

(Received April 2, 1993; revised January 14, 1994)

Abstract. Tukey (1965, Proc. Nat. Acad. Sci. U.S.A., 53, 127–134) introduced linear sensitivity as a measure of informativeness in a collection of order statistics. Here we study its general properties and discuss how it is related to the best linear unbiased estimator, Fisher information measure, and asymptotic relative efficiency. Also, we obtain explicit and asymptotic expressions for the linear sensitivity of a collection of consecutive order statistics from a location or from a scale family, and discuss its role in the comparison of L-estimators. We conclude our discussion with examples from uniform, exponential and normal populations.

Key words and phrases: Linear sensitivity, Fisher information measure, Lestimators, location family, scale family.