###
ESTIMATING FUNCTIONS FOR CONDITIONAL INFERENCE:

MANY NUISANCE PARAMETER CASE

###
H. J. MANTEL^{1} AND V. P. GODAMBE^{2}

^{1} *Social Survey Methods Division, Statistics Canada, Tunney's Pasture,*

Ottawa, Ontario, Canada K1A 0T6

^{2} *Department of Statistics and Actuarial Science, University of Waterloo,*

Waterloo, Ontario, Canada N2L 3G1
(Received January 5, 1990; revised June 10, 1991)

**Abstract.**
When there is a complete sufficient statistic for the
nuisance
parameter which depends on the parameter of interest then there are locally
optimal unbiased estimating functions, but generally there is no globally
optimal estimating function. We consider conditioning on the minimal
sufficient statistic for the nuisance parameter and find the conditional
linear optimal unbiased estimating function. Since the nuisance parameter is
totally eliminated in the conditional model there is no intrinsic problem
in setting up conditional tests of significance and confidence
intervals. A compromise between conditional and unconditional optimum
estimating functions is suggested. The techniques are illustrated on three
examples including the well known common means problem. The
proposed hypothesis testing and confidence interval procedures work
reasonably well for the examples considered.

*Key words and phrases*:
Common means problem, conditional
inference, confidence interval, estimating
function, hypothesis testing, Fisher information, stratified model.

**Source**
( TeX ,
DVI ,
PS )