Abstract
The estimator proposed by Brunk for the indefinite integral of a regression function defined on the unit cube in $\beta$ dimensional Euclidean space is studied. It is shown to be strongly uniformly consistent if the errors satisfy a first moment type of condition and an almost sure rate of convergence of order $O((n/\log_2n)^{-1/2})$ is obtained.
Citation
F. T. Wright. "Sums of Random Variables Indexed by a Partially Ordered Set and the Estimation of Integral Regression Functions." Ann. Statist. 9 (2) 449 - 452, March, 1981. https://doi.org/10.1214/aos/1176345412
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