A study on moment inequalities under a weak dependence

Eunju Hwang, Dong Wan Shin

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Abstract

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.

Original languageEnglish
Pages (from-to)133-141
Number of pages9
JournalJournal of the Korean Statistical Society
Volume42
Issue number1
DOIs
StatePublished - Mar 2013

Bibliographical note

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 .

Keywords

  • Moment inequality
  • Rosenthal-type inequality
  • Weak dependence

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