A central limit theorem for scaled eigenvectors of random dot product graphs
Statistics Theory
2013-12-24 v2 Machine Learning
Statistics Theory
Abstract
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the latent positions, and we show that the appropriately scaled differences between the estimated and true latent positions converge to a mixture of Gaussian random variables. As a corollary, we obtain a central limit theorem for the first eigenvector of the adjacency matrix of an Erd\"os-Renyi random graph.
Cite
@article{arxiv.1305.7388,
title = {A central limit theorem for scaled eigenvectors of random dot product graphs},
author = {Avanti Athreya and Vince Lyzinski and David J. Marchette and Carey E. Priebe and Daniel L. Sussman and Minh Tang},
journal= {arXiv preprint arXiv:1305.7388},
year = {2013}
}
Comments
24 pages, 2 figures