On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling |
| |
Authors: | Reiichiro Kawai |
| |
Institution: | a Department of Mathematics, University of Leicester, Leicester LE1 7RH, UKb Graduate School of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan |
| |
Abstract: | We discuss the local asymptotic behavior of the likelihood function associated with all the four characterizing parameters (α,β,δ,μ) of the Meixner Lévy process under high-frequency sampling scheme. We derive the optimal rate of convergence for each parameter and the Fisher information matrix in a closed form. The skewness parameter β exhibits a slower rate alone, relative to the other three parameters free of sampling rate. An unusual aspect is that the Fisher information matrix is constantly singular for full joint estimation of the four parameters. This is a particular phenomenon in the regular high-frequency sampling setting and is of essentially different nature from low-frequency sampling. As soon as either α or δ is fixed, the Fisher information matrix becomes diagonal, implying that the corresponding maximum likelihood estimators are asymptotically orthogonal. |
| |
Keywords: | 60G51 62E20 |
本文献已被 ScienceDirect 等数据库收录! |
|