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Consistency in Integral Regression Estimation with a Triangular Array of Observation Points

Gordon Pledger
The Annals of Statistics
Vol. 4, No. 1 (Jan., 1976), pp. 234-236
Stable URL: http://www.jstor.org/stable/2958005
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Consistency in Integral Regression Estimation with a Triangular Array of Observation Points
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Abstract

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).

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