The uses of the likelihood function in statistical interference
John Keith Brookhouse · Spiral (Imperial College London) · 1965
The maadmum likelihood, minimum X 2 and minimum legit 1-2 estimators of the parameters are compared with a set of Bayesian estimators in chapter 4. The mean square errors of the estimators were computed conditional upon the experimental outcomes falling in a subset of the sample space.Outcomes falling outside this subset are indicative that the experiment may have been badly designed.The maximum likelihood estimator appears to be superior to the minimum logit )L estimator but inferior to the Rao-Blackwellised minimum logit -X2 estimator.Bayesian estimators of the parameters can be constructed that have a maximum mean square error less than the average mean square error of both the maximum likelihood and minimum logit X2 estimators simultaneously.Aoknowledgements.I would like to thAnk Professor Barnard for suggesting this problem and for many invaluable and stimulating disoussions.