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July, 1974 A Rate of Convergence of a Distribution Connected with Integral Regression Function Estimation
Gary Makowski
Ann. Statist. 2(4): 829-832 (July, 1974). DOI: 10.1214/aos/1176342772

Abstract

Brunk studied integral regression functions and has obtained strong laws and limiting distributions for estimators of these functions. In this note we will study additional conditions that ensure a rate of convergence of the distribution function of the maximum absolute difference of an integral regression function and its estimator, suitably normalized, to the distribution function of a normalized maximum absolute value of partial sums of random variables. These results are corollaries of convergence results obtained by Sawyer and Rosenkrantz.

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Gary Makowski. "A Rate of Convergence of a Distribution Connected with Integral Regression Function Estimation." Ann. Statist. 2 (4) 829 - 832, July, 1974. https://doi.org/10.1214/aos/1176342772

Information

Published: July, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0285.62017
MathSciNet: MR378223
Digital Object Identifier: 10.1214/aos/1176342772

Subjects:
Primary: 60F05
Secondary: 60G50 , 62G05 , 62G10

Keywords: independent observations regression model , Integral regression function , maximum absolute value of partial sum

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 4 • July, 1974
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