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STEIN-TYPE IMPROVEMENTS OF CONFIDENCE INTERVALS

FOR THE GENERALIZED VARIANCE

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SANAT K. SARKAR

*Department of Statistics, Temple University, Philadelphia, PA 19122, U.S.A.*
(Received October 24, 1989; revised March 19, 1990)

**Abstract.**
Based on independent random matices *X*: *p* ×
*m* and *S*: *p* × *p* distributed, respectively, as *N*_{pm}(*mu*,
*Sigma* \otimes *I*_{m}) and *W*_{p}(*n*, *Sigma*) with *mu* unknown and *n* __>__ *p*,
the problem of obtaining confidence interval for |*Sigma*| is
considered. Stein's idea of improving the best affine equivariant point
estimator of |*Sigma*| has been adapted to the interval estimation
problem. It is shown that an interval estimator of the form
|*S*|(*b*^{-1}, *a*^{-1}) can be improved by min{|*S*|,
c|*S* + *XX*'|}(*b*^{-1}, *a*^{-1}) for a certain constant
*c* depending on (*a*, *b*).

*Key words and phrases*:
Generalized variance, invariant
interval estimators, Stein-type improvements.

**Source**
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