EXPANSIONS FOR STATISTICS INVOLVING THE MEAN ABSOLUTE DEVIATIONS

GUTTI JOGESH BABU AND C. RADHAKRISHNA RAO

Statistics Department, 219 Pond Laboratory, Pennsylvania State University, University Park, PA 16802, U.S.A.

(Received May 22, 1990; revised October 1, 1990)

Abstract. Expansion for the difference of mean absolute deviations from the sample mean and the population mean is derived. This result is used to obtain strong representations for mean absolute deviations from the sample mean and the sample median. Edgeworth expansions for some scale invariant statistics involving the mean absolute deviations are studied. These expansions are shown to be valid in spite of the presence of a lattice variable.

Key words and phrases: Mean absolute deviations, Edgeworth expansions, quantiles, linear model, L_{1}-norm.