ON FISHER INFORMATION INEQUALITIES IN THE PRESENCE OF NUISANCE PARAMETERS

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.