Empirical likelihood for compound Poisson processes under infinite second moment

Conghua Cheng, Zhi Liu and Yi Wan

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 17, 8618-8627

Abstract: The compound Poisson process SN(t)=∑j=1N(t)Xj$S_{N(t)}=\sum \nolimits _{j=1}^{N(t)}X_j$ has been widely used in many fields, for example, physics, engineering, finance, and so on. Regarding the process, the average number, namely t− 1E[SN(t)] = λμ, attracts lots of interests. In this article, we derive the limiting behavior of the log empirical likelihood ratio statistic for λμ when the population is in the domain of attraction of normal law. The simulation studies confirm the theoretical result.

Date: 2017
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DOI: 10.1080/03610926.2016.1185122

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