Adaptivity and optimality of the monotone least-squares estimator
Adaptivity and optimality of the monotone least-squares estimator
In this paper, we will consider the estimation of a monotone regression (or density) function in a fixed point by the least-squares (Grenander) estimator. We will show that this estimator is locally asymptotic minimax, in the sense that, for each $f_0$, the attained rate of the probabilistic error is uniform …