A simple variance inequality for U-statistics of a Markov chain with applications
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the Markov Chain. We apply this result to derive the strong law of large numbers for U-statistics of a Markov Chain under conditions which are close to being optimal.
Volume (Year): 82 (2012)
Issue (Month): 6 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Harel, Michel & Puri, Madan L., 1990. "Weak invariance of generalized u-statistics for nonstationary absolutely regular processes," Stochastic Processes and their Applications, Elsevier, vol. 34(2), pages 341-360, April.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1193-1201. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.