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Consistency in Integral Regression Estimation with a Triangular Array of Observation Points
The Annals of Statistics
Vol. 4, No. 1 (Jan., 1976), pp. 234-236
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2958005
Page Count: 3
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Let μ be a continuous mean regression function defined on U, the unit cube in N-dimensional Euclidean space. Let F be a distribution function with support in U, and let M denote the indefinite integral of μ with respect to F. This paper provides consistency results, including rates of convergence, for a certain estimator of M in the case that the nth estimate is based on observations at points tn1,⋯, tnn of U. The estimator is the N-dimensional analogue of that considered by Brunk (1970).
The Annals of Statistics © 1976 Institute of Mathematical Statistics