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EXPANSIONS FOR STATISTICS INVOLVING THE MEAN

ABSOLUTE DEVIATIONS

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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.

**Source**
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