Some remarks on MCMC estimation of spectra of integral operators

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. Giné 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.

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)

References in corpus (4)

• Consistency of spectral clustering
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Quantitative bounds on convergence of time-inhomogeneous Markov chains
• On nonlinear Markov chain Monte Carlo

Cited by in corpus (2)

• From random matrices to long range dependence
• Consistent estimation of the spectrum of trace class data augmentation algorithms