and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum … likelihood estimator. It is well known that the performance of the estimator is depending on the choice of a smoothing parameter …

estimating multivariate derivatives is complicated. In this paper, an estimator of multivariate second derivative is obtained via … local quadratic regression with cross terms left out. This estimator has the optimal rate of convergence but is simpler and … uses a lot less computing time than the full local quadratic estimator. Using this as a pilot estimator, an estimator of …