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A Bernstein type inequality and moderate deviations for weakly dependent sequences
Open accessAbstract
In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations.
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Cited by
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Fan, J., Liao, Y., & Mincheva, M. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12016 · Cited by 909
Grouped Patterns of Heterogeneity in Panel Data
Bonhomme, S., & Manresa, E. (2015) · Econometrica · doi:10.3982/ecta11319 · Cited by 451
Sparse principal component analysis for high-dimensional stationary time series
Fujimori, K., Goto, Y., Liu, Y., & Taniguchi, M. (2023) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12664 · Cited by 7
Metadata
- Authors
- Merlevède, F., Peligrad, M., & Rio, E.
- Venue
- Probability Theory and Related Fields
- Published
- 2010-06-09
- Volume
- 151
- Issue
- 3-4
- Pages
- 435-474
- ISSN
- 0178-8051 (ISSN-L)
- 1432-2064
- OpenAlex
- W2040163842
- Cited by
- 178
- References
- 0
- FWCI
- 3.77
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: A Bernstein type inequality and moderate deviations for weakly dependent sequences. https://app.cochat.ai/papers/10.1007/s00440-010-0304-9
- The paper
- Merlevède, F., Peligrad, M., & Rio, E. (2011). A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-010-0304-9
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