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ON FISHER INFORMATION INEQUALITIES IN THE PRESENCE

OF NUISANCE PARAMETERS

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VASANT P. BHAPKAR AND CIDAMBI SRINIVASAN

*Department of Statistics, University of Kentucky, 817 Patterson Office Tower,*

Lexington, KY 40506-0027, U.S.A.
(Received August 7, 1991; revised November 12, 1993)

**Abstract.**
The existence of a generalized Fisher
information matrix for a vector parameter of interest is established
for the case where nuisance parameters are present under general
conditions. A matrix inequality is established for the information
in an estimating function for the vector parameter of interest. It is
shown that this inequality leads to a sharper lower bound for the
variance matrix of unbiased estimators, for any set of functionally
independent functions of parameters of interest, than the lower bound
provided by the Cramér-Rao inequality in terms of the full
parameter.

*Key words and phrases*:
Information matrix, partial
sufficiency, partial ancillarity, estimating functions.

**Source**
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