The Annals of Statistics

Laws of the Iterated Logarithm for Permuted Random Variables and Regression Applications

Gary G. Makowski

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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.

Article information

Source
Ann. Statist., Volume 1, Number 5 (1973), 872-887.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342508

Digital Object Identifier
doi:10.1214/aos/1176342508

Mathematical Reviews number (MathSciNet)
MR343358

Zentralblatt MATH identifier
0272.60028

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 60G45 60G50: Sums of independent random variables; random walks

Keywords
Iterated logarithm order preserving permutation maximum of partial sum semimartingale integral regression non-decreasing regression Galtonian regression

Citation

Makowski, Gary G. Laws of the Iterated Logarithm for Permuted Random Variables and Regression Applications. Ann. Statist. 1 (1973), no. 5, 872--887. doi:10.1214/aos/1176342508. https://projecteuclid.org/euclid.aos/1176342508


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