MINIMAX BAYES ESTIMATION IN NONPARAMETRIC REGRESSION

One observes n data points, (t(i), Y(i)), with the mean of Y(i), conditional on the regression function f, equal to f(t(i)). The prior distribution of the vector f = (f(t1),..., f(t(n)))t is unknown, but ties in a known class-OMEGA. An estimator, f, of f is found which minimizes the maximum E parallel-to f - f parallel-to 2. The maximum is taken over all priors in OMEGA and the minimum is taken over linear estimators of f. Asymptotic properties of the estimator are studied in the case that t(i) is one-dimensional and OMEGA is the set of priors for which f is smooth.