Cp. Robert et Jtg. Hwang, MAXIMUM-LIKELIHOOD-ESTIMATION UNDER ORDER RESTRICTIONS BY THE PRIOR FEEDBACK METHOD, Journal of the American Statistical Association, 91(433), 1996, pp. 167-172
Algorithms for deriving isotonic regression estimators id order-restri
cted linear models and more generally restricted maximum likelihood es
timators are usually quite dependent on the particular problem conside
red. We propose here an optimization method based on a sequence of for
mal Bayes estimates whose variances converge to zero. This method, aki
n to simulated annealing, can be applied ''universally''; that is, as
long as these Bayes estimators can be derived by exact computation or
Markov chain Monte Carlo sampling approximation. We then give an illus
tration of our method for two real-life examples.