Estimating beta-mixing coefficients

Estimating beta-mixing coefficients

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by Daniel J. Mcdonald , Cosma Rohilla , Shalizi Mark Schervish

BibTeX

@MISC{Mcdonald_estimatingbeta-mixing,
    author = {Daniel J. Mcdonald and Cosma Rohilla and Shalizi Mark Schervish},
    title = {Estimating beta-mixing coefficients},
    year = {}
}

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Abstract

The literature on statistical learning for time series assumes the asymptotic independence or “mixing ” of the data-generating process. These mixing assumptions are never tested, and there are no methods for estimating mixing rates from data. We give an estimator for the beta-mixing rate based on a single stationary sample path and show it is L1-risk consistent. 1

Citations

419	Probability and Statistics - DeGroot, Schervish
319	On the method of bounded differences - McDiarmid - 1989
173	Mixing. Properties and examples - Doukhan - 1994
124	Stability and generalization - Bousquet, Elisseeff - 2002
67	Learning and Generalization: With Applications to Neural Networks - Vidyasagar - 2003
52	On some global measures of the deviations of density function estimates, The Annals of Statistics 1 - Bickel, Rosenblatt - 1973
45	Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. The Annals of Statistics 6 - Silverman - 1978
32	N.: 2000, The Nature of Statistical Learning Theory, Statistics for Engineering and Information Science, 2nd edn - Vapnik
31	Rates of convergence for empirical processes of stationary mixing sequences. The Annals of Probability - Yu - 1994
26	Nonparametric Time Series Prediction Through Adaptive Model Selection - Meir - 2000
23	Basic properties of strong mixing conditions: a survey and some open questions - Bradley - 2005
19	Nonparametric Density Estimation: The L1 - Devroye, Györfi - 1985
16	Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Stochastic Process - Nummelin, Tuominen - 1982
10	Hypothesis testing for families of ergodic processes - Nobel - 2006
9	Convergence and consistency of regularized boosting algorithms with stationary β-mixing observations - Lozano, Kulkarni, et al. - 2006
7	Adaptive estimation in autoregression or β-mixing regression via model selection. The Annals of Statistics - Baraud, Compte, et al. - 2001
7	Measure Theory (Graduate Texts in Mathematics no - Halmos - 1961
7	Density Estimation in the L∞ Norm for Dependent Data with Applications to the Gibbs Sampler - Yu - 1993
5	2002) “Mixing and Moment - Carrasco, Chen
5	Mixing properties of ARMA processes,” Stochastic Process - Mokkadem - 1988
4	Probably Approximately Correct Learning with Beta-Mixing Input Sequences - Karandikar, Vidyasagar - 2009
2	On the Maximum Deviation Between the Histogram and the Underlying Density,” Probability Theory and Related Fields - Freedman, Diaconis - 1981
2	Stability Bounds for Stationary ϕ-mixing and βmixing - Mohri, Rostamizadeh - 2010
2	The L1 convergence of kernel density estimates under dependence - Tran, T - 1989
2	On the maximum deviation of the sample density - Woodroofe - 1967
1	Weak Dependence - Dedecker, Doukhan, et al. - 2007
1	Chromatic PAC-Bayes Bounds for NonIID Data: Applications to Ranking and Stationary β-Mixing Processes - Ralaivola, Szafranski, et al. - 2010