Nonparametric curve estimation with Bernstein estimates (Q1359946)

For the estimation of the regression function in a random design model a Bernstein type estimator is proposed. The author studies various local and global asymptotic properties of this estimator: Consistency and asymptotic normality at a fixed point are proved and an asymptotic expression for the expectation of the estimator is derived. Further, an asymptotic expansion for the expectation of a quadratic deviation of the estimator is given; this criterion can be regarded as a modification of the mean integrated squared error. Finally, sufficient conditions for strong consistency, measured in \(L_1\)- and sup- norm are presented.