English

Some remarks on MCMC estimation of spectra of integral operators

Probability 2015-09-21 v3

Abstract

We prove a law of large numbers for empirical approximations of the spectrum of a kernel integral operator by the spectrum of random matrices based on a sample drawn from a Markov chain, which complements the results by V. Koltchinskii and E. Gin\'{e} for i.i.d. sequences. In a special case of Mercer's kernels and geometrically ergodic chains, we also provide exponential inequalities, quantifying the speed of convergence.

Keywords

Cite

@article{arxiv.1311.7566,
  title  = {Some remarks on MCMC estimation of spectra of integral operators},
  author = {Radosław Adamczak and Witold Bednorz},
  journal= {arXiv preprint arXiv:1311.7566},
  year   = {2015}
}

Comments

Published at http://dx.doi.org/10.3150/14-BEJ635 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)