THE INTEGRATED MEAN SQUARED ERROR OF SERIES REGRESSION AND A ROSENTHAL HILBERT-SPACE INEQUALITY
为非参数序列回归估计量（包括最小二乘和平均最小二乘）的积分均方误差开发了统一近似，并将罗森塔尔概率不等式推广到希尔伯特空间值随机变量。
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, Israel Journal of Mathematics 8, 273–303; 1972, Sixth Berkeley Symposium on Mathematical Statistics and Probability , vol. 2, pp. 149–167. University of California Press) to the case of Hilbert-space valued random variables.