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September, 1973 Laws of the Iterated Logarithm for Permuted Random Variables and Regression Applications
Gary G. Makowski
Ann. Statist. 1(5): 872-887 (September, 1973). DOI: 10.1214/aos/1176342508

Abstract

In this paper Laws of the Iterated Logarithm for maximums of absolute values of partial sums of permuted random variables are derived under conditions that are the same as or similar to conditions used by Kolmogorov, Hartman and Wintner, Petrov and Csaki in deriving Laws of the Iterated Logarithm for sums of random variables or semimartingales. These results are then applied to obtain logarithmic convergence rates for estimators of non-decreasing regression functions and integral regression functions.

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Gary G. Makowski. "Laws of the Iterated Logarithm for Permuted Random Variables and Regression Applications." Ann. Statist. 1 (5) 872 - 887, September, 1973. https://doi.org/10.1214/aos/1176342508

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0272.60028
MathSciNet: MR343358
Digital Object Identifier: 10.1214/aos/1176342508

Subjects:
Primary: 60F99
Secondary: 60G45, 60G50

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • September, 1973
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