Description:
<jats:p>This paper develops uniform approximations for the integrated mean squared error (IMSE) of nonparametric series regression estimators, including both least-squares and averaging least-squares estimators. To develop these approximations, we also generalize an important probability inequality of Rosenthal (1970,<jats:italic>Israel Journal of Mathematics</jats:italic>8, 273–303; 1972,<jats:italic>Sixth Berkeley Symposium on Mathematical Statistics and Probability</jats:italic>, vol. 2, pp. 149–167. University of California Press) to the case of Hilbert-space valued random variables.</jats:p>