Nonparametric estimation of a linear functional of the regression function for a given observation design (Q1122264)

The authors consider the problem of nonparametric estimation for a linear functional of regression when \((t_ 1,t_ 2,...,t_ n)\) represent given observations so that \(t_ 1,t_ 2,...,t_ n\) are independent variables with the same known probability density. A lower bound on the estimation accuracy is found and an estimator achieving this bound asymptotically is constructed.