An effective bandwidth selection method for local linear regression is proposed in Fan and Gijbels [1995, J. Roy. Statist. Soc. Ser. B, 57, 371-394]. The method is based on the idea of the pre-asymptotic substitution and has been tested extensively. This paper investigates the rate of...

Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(h2n). In this note, a method of correcting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, this...