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.
Citation
Radosław Adamczak. Witold Bednorz. "Some remarks on MCMC estimation of spectra of integral operators." Bernoulli 21 (4) 2073 - 2092, November 2015. https://doi.org/10.3150/14-BEJ635
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