### 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.

Original language | English |
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Pages (from-to) | 460-469 |

Number of pages | 10 |

Journal | Statistics and Probability Letters |

Volume | 81 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling.** / Kawai, Reiichiro; Masuda, Hiroki.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 81, no. 4, pp. 460-469. https://doi.org/10.1016/j.spl.2010.12.011

}

TY - JOUR

T1 - On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling

AU - Kawai, Reiichiro

AU - Masuda, Hiroki

PY - 2011/4/1

Y1 - 2011/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78651374936&partnerID=8YFLogxK

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U2 - 10.1016/j.spl.2010.12.011

DO - 10.1016/j.spl.2010.12.011

M3 - Article

AN - SCOPUS:78651374936

VL - 81

SP - 460

EP - 469

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 4

ER -