TY - JOUR
T1 - A study on moment inequalities under a weak dependence
AU - Hwang, Eunju
AU - Shin, Dong Wan
N1 - Funding Information:
The authors are grateful for useful comments of two anonymous referees. This work was supported partly by Priority Research Centers Program ( 2009-0093827 ), and partly by Basic Research Program ( 2010-0023000 ) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology .
PY - 2013/3
Y1 - 2013/3
N2 - We establish Roussas-Ioannides-type inequalities [Roussas, G. G., & Ioannides, D. A. (1987). Moment inequalities for mixing sequences of random variables. Stochastic Analysis and Applications, 5, 61-120] under general ψ-weak dependence proposed by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 84, 313-342], which unifies weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. Simple applications of the inequalities extend many important moment inequalities available in the literature for mixing sequences to those for ψ-weakly dependent sequences. As an illustration, the established inequalities are applied to extend the result for moment bound of partial sum under strong mixing by Cox and Kim [Cox, D. D., & Kim, T. Y. (1995). Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic Process and their Applications, 56, 151-158] to the class of ψ-weakly dependent processes.
AB - We establish Roussas-Ioannides-type inequalities [Roussas, G. G., & Ioannides, D. A. (1987). Moment inequalities for mixing sequences of random variables. Stochastic Analysis and Applications, 5, 61-120] under general ψ-weak dependence proposed by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 84, 313-342], which unifies weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. Simple applications of the inequalities extend many important moment inequalities available in the literature for mixing sequences to those for ψ-weakly dependent sequences. As an illustration, the established inequalities are applied to extend the result for moment bound of partial sum under strong mixing by Cox and Kim [Cox, D. D., & Kim, T. Y. (1995). Moment bounds for mixing random variables useful in nonparametric function estimation. Stochastic Process and their Applications, 56, 151-158] to the class of ψ-weakly dependent processes.
KW - Moment inequality
KW - Rosenthal-type inequality
KW - Weak dependence
UR - http://www.scopus.com/inward/record.url?scp=84872379847&partnerID=8YFLogxK
U2 - 10.1016/j.jkss.2012.06.003
DO - 10.1016/j.jkss.2012.06.003
M3 - Article
AN - SCOPUS:84872379847
SN - 1226-3192
VL - 42
SP - 133
EP - 141
JO - Journal of the Korean Statistical Society
JF - Journal of the Korean Statistical Society
IS - 1
ER -