Abstract
In this paper, a Hoeffding-type inequality is presented for a class of ergodic time series. The inequality is then used to construct uniformly exponentially consistent tests, which are useful tools for studying Bayesian consistency.
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Azuma, K.: Weighted sums of certain dependent random variables. Tôhoku Math. J. 19(3), 357–367 (1967)
Glynn, P., Ormoneit, D.: Hoeffding’s inequality for uniformly ergodic Markov chains. Stat. Probab. Lett. 56, 143–146 (2002)
Herkenrath, U.: On the uniform ergodicity of Markov processes of order 2. J. Appl. Probab. 40(2), 455–472 (2003)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58, 13–30 (1963)
McDiarmid, C.: On the method of bounded differences. In: Siemons, J. (ed.) Surveys in Combinatorics, pp. 148–188. Cambridge Univ. Press, Cambridge (1989)
Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Springer, New York (1993)
Schwartz, L.: On Bayes procedures. Z. Wahrsch. Verw. Gebiete 4, 10–26 (1965)
van de Geer, S.: On Hoeffding’s inequality for dependent random variables. In: Dehling, H., Mikosch, T., Sørensen, M. (eds.) Empirical Process Techniques for Dependent Data, pp. 161–170. Birkhäuser, Boston (2002)
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Tang, Y. A Hoeffding-Type Inequality for Ergodic Time Series. J Theor Probab 20, 167–176 (2007). https://doi.org/10.1007/s10959-007-0057-2
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DOI: https://doi.org/10.1007/s10959-007-0057-2