Empirical Quantile CLTs For Some Self-Similar Processes
Probability
2013-08-21 v1 Statistics Theory
Statistics Theory
Abstract
In a paper of Jason Swanson, a CLT for the sample median of independent Brownian motions with value 0 at 0 was proved. Here we extend this result in two ways. We prove such a result for a collection of self-similar processes which include the fractional Brownian motions, all stationary, independent increment symmetric stable processes tied down at 0 as well as iterated and integrated Brownian motions. Second, our results hold uniformly over all quantiles in a compact sub-interval of (0,1). We also examine sample function properties connected with these CLTs.
Keywords
Cite
@article{arxiv.1308.4194,
title = {Empirical Quantile CLTs For Some Self-Similar Processes},
author = {James Kuelbs and Joel Zinn},
journal= {arXiv preprint arXiv:1308.4194},
year = {2013}
}
Comments
24 pages. arXiv admin note: text overlap with arXiv:1111.4591