Minimax Linear Estimation in a White Noise Problem

Linear estimation of f(x) at a point in a white noise model is considered. The exact linear minimax estimator of f(0) is found for the family of f(x) in which f′(x) is Lip (M). The resulting estimator is then used to verify a conjecture of Sacks and Ylvisaker concerning the near optimality of the Epanechnikov kernel.