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Title: On the Local Asymptotic Behavior of the Likelihood Function for Meixner Lévy Processes under High-Frequency Sampling
Authors: Kawai, Reiichiro
Masuda, Hiroki
First Published: 24-Dec-2010
Publisher: Elsevier
Citation: Statistics and Probability Letters, 2011, 81 (4), pp. 460-469
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.
DOI Link: 10.1016/j.spl.2010.12.011
ISSN: 0167-7152
Type: Article
Rights: This is the author’s final draft of the paper published as Statistics and Probability Letters, 2011, 81 (4), pp. 460-469. The final published version is available at, Doi: 10.1016/j.spl.2010.12.011.
Appears in Collections:Published Articles, Dept. of Mathematics

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