Abstract
This chapter considers various generalizations of the results surveyed in this volume, as well as some open problems. In particular, generalizations to distances other than the distributional distance are considered, as well as non-stationary processes and processes more general than time series, such as multidimensional processes and processes on infinite random graphs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Terrence M. Adams and Andrew B. Nobel. Uniform approximation of Vapnik-Chervonenkis classes. Bernoulli, 18(4):1310–1319, 2012.
David Aldous and Russell Lyons. Processes on unimodular random networks. Electron. J. Probab., 12:no. 54, 1454–1508, 2007.
Itai Benjamini and Nicolas Curien. Ergodic theory on stationary random graphs. Electron. J. Probab., 17:no. 93, 1–20, 2012.
András Gyorgy, Tamás Linder, and Gábor Lugosi. Efficient tracking of large classes of experts. IEEE Transactions on Information Theory, 58(11):6709–6725, 2012.
L. V. Kantorovich and G. S. Rubinstein. On a function space in certain extremal problems. Dokl. Akad. Nauk USSR, 115(6):1058–1061, 1957.
A.N. Kolmogorov. Sulla determinazione empirica di una legge di distribuzione. G. Inst. Ital. Attuari, pages 83–91, 1933.
Ulrich Krengel. Ergodic Theorems. Walter de Gruyter, Berlin, New York, 1985.
Russell Lyons and Yuval Peres. Probability on trees and networks, volume 42. Cambridge University Press, 2016.
D.S. Ornstein and B. Weiss. How sampling reveals a process. Annals of Probability, 18(3):905–930, 1990.
D. Ryabko. Hypotheses testing on infinite random graphs. In Proceedings of the 28th International Conference on Algorithmic Learning Theory (ALT’17), volume 76 of PMLR, pages 400–411, Kyoto, Japan, 2017. JMLR.
Daniil Ryabko and Jeremie Mary. A binary-classification-based metric between time-series distributions and its use in statistical and learning problems. Journal of Machine Learning Research, 14:2837–2856, 2013.
P. Shields. The Ergodic Theory of Discrete Sample Paths. AMS Bookstore, 1996.
Frans MJ Willems. Coding for a binary independent piecewise-identically-distributed source. IEEE Transactions on Information Theory, 42(6):2210–2217, 1996.
V. M. Zolotarev. Probability metrics. Theory of Probability and Its Applications., 28(2):264–287, 1983.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ryabko, D. (2019). Generalizations. In: Asymptotic Nonparametric Statistical Analysis of Stationary Time Series. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-12564-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-12564-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12563-9
Online ISBN: 978-3-030-12564-6
eBook Packages: Computer ScienceComputer Science (R0)