## The Annals of Statistics

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

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

#### 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