A central limit theorem for scaled eigenvectors of random dot product graphs
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 Erdös-Renyi random graph.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2013
- DOI:
- 10.48550/arXiv.1305.7388
- arXiv:
- arXiv:1305.7388
- Bibcode:
- 2013arXiv1305.7388A
- Keywords:
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- Mathematics - Statistics Theory;
- Statistics - Machine Learning
- E-Print:
- 24 pages, 2 figures