T. Wright, F., Sums of random variables indexed by a partially ordered set and the estimation of integral regression functions, Annals of statistics , 9(2), 1981, pp. 449-452
The estimator proposed by Brunk for the indefinite integral of a regression function defined on the unit cube in β 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/log2n)−1/2)is obtained.