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A Note on Exponential Inequalities of ψ-Weakly Dependent Sequences
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 Title & Authors
A Note on Exponential Inequalities of ψ-Weakly Dependent Sequences
Hwang, Eunju; Shin, Dong Wan;
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 Abstract
Two exponential inequalities are established for a wide class of general weakly dependent sequences of random variables, called -weakly dependent process which unify weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The -weakly dependent process includes, for examples, stationary ARMA processes, bilinear processes, and threshold autoregressive processes, and includes essentially all classes of weakly dependent stationary processes of interest in statistics under natural conditions on the process parameters. The two exponential inequalities are established on more general conditions than some existing ones, and are proven in simpler ways.
 Keywords
Weak dependence exponential inequality;Bernstein-type inequality;partial sum of random variables;
 Language
English
 Cited by
1.
Kernel estimators of mode under $$\psi $$ ψ -weak dependence, Annals of the Institute of Statistical Mathematics, 2016, 68, 2, 301  crossref(new windwow)
 References
1.
Ango Nze, P., Buhlmann, P. and Doukhan, P. (2002). Nonparametric regression estimation under weak dependence beyond mixing and association, The Annals of Statistics, 30, 397-430. crossref(new window)

2.
Ango Nze, P. and Doukhan, P. (2004). Weak dependence: Models and applications to econometrics, Econometric Theory, 20, 995-1045.

3.
Coulon-Prieur, C. and Doukhan, P. (2000). A triangular central limit theorem under a new weak dependent condition, Statistics & Probability Letters, 47, 61-68. crossref(new window)

4.
Dedecker, J. and Prieur, C. (2004). Coupling for $\tau$-dependent sequences and applications, Journal of Theoretical Probability, 17, 861-885. crossref(new window)

5.
Dedecker, J., Doukhan, P., Lang, G., Le'on, R., Jose Rafael, R., Louhichi, S. and Prieur, C. (2007). Lecture Notes in Statistics, 190, Weak dependence: with examples and applications, Springer, New York.

6.
Doukhan, P. and Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities, Stochastic Processes & Their Applications, 84, 313-342. crossref(new window)

7.
Doukhan, P. and Louhichi, S. (2001). Functional estimation of a density under a new weak dependence condition, Scandinavian Journal of Statistics, 28, 325-341. crossref(new window)

8.
Doukhan, P. and Neumann, M. H. (2007). Probability and moment inequalities for sums of weakly dependent random variables with applications, Stochastic Processes & Their Applications, 117, 878-903. crossref(new window)

9.
Doukhan, P. and Neumann, M. H. (2008). The notion of $\psi$-weak dependence and its applications to bootstrapping time series, Probability Surveys, 5, 146-168. crossref(new window)

10.
Hwang, E. and Shin, D.W. (2011). Semiparametric estimation for partially linear models with $\psi$-weak dependent errors, Journal of the Korean Statistical Society, 40, 411-424. crossref(new window)

11.
Hwang, E. and Shin, D. W. (2012a). Stationary bootstrap for kernel density estimators under $\psi$-weak dependence, Computational Statistics and Data Analysis, 56, 1581-1593. crossref(new window)

12.
Hwang, E. and Shin, D. W. (2012b). Strong consistency of the stationary bootstrap under $\psi$-weak dependence, Statistics and Probability Letters, 82, 488-495. crossref(new window)

13.
Hwang, E. and Shin, D. W. (2013a). A study on moment inequalities under a weak dependence, Journal of the Korean Statistical Society, 42, 133-141. crossref(new window)

14.
Hwang, E. and Shin, D. W. (2013b). Kernel estimators of mode under $\psi$-weak dependence, The Annals of the Institute of Statistical Mathematics, in revision.

15.
Kallabis, R. S. and Neumann, M. H. (2006). An exponential inequality under weak dependence, Bernoulli, 12, 333-350. crossref(new window)