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STATISTICAL INFERENCE BASED ON ALIGNED RANKS

FOR TWO-WAY MANOVA WITH INTERACTION

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TAKA-AKI SHIRAISHI

*Department of Mathematics, Yokohama City University, Yokohama 236, Japan*
(Received May 31, 1988; revised June 13, 1990)

**Abstract.**
Multiresponse experiments in two-way layouts
with interactions, having equal number of observations per cell, are
considered. Robust procedures based on aligned ranks for statistical
inference of interactions, main effects and an overall mean response
in the models are proposed. Large sample properties of the proposed
tests, estimators and confidence regions as the cell size tends to
infinity are investigated. For the univariate case, it is found that
the asymptotic relative efficiencies (ARE's) of the proposed procedures
relative to classical procedures agree with the ARE-results of the
two-sample rank test relative to the t-test. In addition, robustness
due to Huber (1981, *Robust Statistics*, Wiley, New York) can
be drawn.

*Key words and phrases*:
Asymptotically distribution-free
procedure, multivariate analysis, test, point estimate, confidence
region, asymptotic efficiency, robustness.

**Source**
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