A note on concentration inequalities for the overlapped batch mean variance estimators for Markov chains
In this paper, we study the concentration properties of quadratic forms associated with Markov chains using the martingale decomposition method introduced by Atchad\'e and Cattaneo (2014). In particular, we derive concentration inequalities for the overlapped batch mean (OBM) estimators of the asymptotic variance for uniformly geometrically ergodic Markov chains. Our main result provides an explicit control of the $p$-th moment of the difference between the OBM estimator and the asymptotic variance of the Markov chain with explicit dependence upon $p$ and mixing time of the underlying Markov chain.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors…
Concentration Inequalities for Statistical Inference
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, fro…
Liquidity, risk measures, and concentration of measure
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(\rho(\lambda X))_…
Concentration Inequalities for Bounded Random Vectors
We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Diri…
Uniform-in-time concentration in two-layer neural networks via transportation inequalities
We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and their mean-field limit, for quadratic los…