MAXIMAL INEQUALITIES AND AN APPLICATION UNDER A WEAK DEPENDENCE

Title & Authors
MAXIMAL INEQUALITIES AND AN APPLICATION UNDER A WEAK DEPENDENCE
HWANG, EUNJU; SHIN, DONG WAN;

Abstract
We establish maximal moment inequalities of partial sums under $\small{{\psi}}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with $\small{{\psi}}$-weakly dependent innovations.
Keywords
weak dependence;maximal moment inequality;linear process;functional central limit theorem;
Language
English
Cited by
1.
Stationary bootstrapping for common mean change detection in cross-sectionally dependent panels, Metrika, 2017, 80, 6-8, 767
References
1.
P. Ango Nze, P. Buhlmann, and P. Doukhan, Weak dependence beyond mixing and asymptotics for nonparametric regression, Ann. Statist. 30 (2002), no. 2, 397-430.

2.
P. J. Bickel and P. Bulmann, A new mixing notion and functional central limit theorems for a sieve bootstrap in time series, Bernoulli 5 (1999), no. 3, 413-446.

3.
J. Dedecker and P. Doukhan, A new covariance inequality and applications, Stochastic Process. Appl. 106 (2003), no. 1, 63-80.

4.
J. Dedecker, P. Doukhan, G. Lang, R. Leon, R. Jose Rafael, S. Louhichi, and C. Prieur, Weak dependence: with examples and applications, Lecture Notes in Statistics, 190, Springer, New York, 2007.

5.
P. Doukhan and S. Louhichi, A new weak dependence condition and applications to moment inequalities, Stochastic Process. Appl. 84 (1999), no. 2, 313-342.

6.
P. Doukhan and M. H. Neumann, Probability and moment inequalities for sums of weakly dependent random variables with applications, Stochastic Process. Appl. 117 (2007), no. 7, 878-903.

7.
E. Hwang and D. W. Shin, A study on moment inequalities under a weak dependence, J. Korean Statist. Soc. 42 (2013), no. 1, 133-141.

8.
S. Lee, Random central limit theorem for the linear process generated by a strong mixing process, Statist. Probab. Lett. 35 (1997), no. 2, 189-196.

9.
B. L. S. Prakasa Rao, Random central limit theorems for martingales, Acta. Math. Acad. Sci. Hungar. 20 (1969), 217-222.

10.
A. Reyni, On the central limit theorem for the sum of a random number of independent random variables, Acta. Math. Acad. Sci. Hungar. 11 (1960), 97-102.

11.
G. G. Roussas and D. A. Ioannides, Moment inequalities for mixing sequences of random variables, Stochastic Anal. Appl. 5 (1987), no. 1, 61-120.

12.
S. Utev and M. Peligrad, Maximal inequalities and an invariance principle for a class of weakly dependent random variables, J. Theoret. Probab. 16 (2003), no. 1, 101-115.

13.
G. Xing, S. Yang, and A. Chen, A maximal moment inequaltiy for $\alpha$-mixing sequences and its applications, Statist. Probab. Lett. 79 (2009), 1429-1437.

14.
W. Xuejun, H. Shuhe, S. Yan, and Y.Wenzhi, Moment inequality for $\varphi$-mixing sequences and its applications, J. Inequal. Appl. (2009), Art. ID 379743, 12 pp.

15.
S. C. Yang, Maximal moment inequalty for partial sums of strong mixing sequences and applications, Acta Math. Sin. (Eng. Ser.) 23 (2007), 1013-1024.