Robustness of the Profile Likelihood of a Parameter of Interest 
	   Eloisa Diaz-Frances
	   diazfran@cimat.mx
Department of Probability and Statistics
Centro de Investigacion en Matematicas
Guanajuato, 36000, Mexico
(This is joint work with David A. Sprott and Jose. Montoya).

      The profile likelihood function is frequently used to estimate 
a parameter of interest separately from the remaining nuisance parameters 
in the model to be considered. It is obtained by replacing the nuisance 
parameters in the likelihood function by their restricted maximum 
likelihood estimates corresponding to fixed values of the parameters 
of interest. Thus this assumes great precision in the estimation of the 
nuisance parameters. We explore here the changes that the profile likelihood 
may take under small perturbations in the estimation of the nuisance 
parameters. In most cases, the profile likelihood results robust under 
these slight changes. However non robust cases are easily detected and 
turn out to be indicative of problematic situations that might require 
careful treatment, and where the profile likelihood might not be 
informative or reliable.

      For instance, the Binomial (N,p) model provides an example for both 
cases, robust and non-robust. The Binomial model is widely used in Ecology 
to estimate animal abundance. A biological example with non robust profile 
likelihood of N that was analyzed in Carroll and Lombard (1985) is considered, 
the number of impala herds in a small area of the Kruger Park in South Africa.  
A control regular example with robust profile likelihood is also presented 
for comparison.

Carroll, R. J. and Lombard, F. (1985). JASA, V.80, No. 390, pp.423-426.