## ＜プレプリント＞Likelihood Estimation of Stable Levy Processes from Discrete Data

作成者 著者識別子 作成者名 所属機関 所属機関名 Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院 英語 Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院 2006-04-10 2006-18 Author's Original open access We study the likelihood inference for real-valued non-Gaussian stable Levy processes $X = (X_t)_{t in R_+}$ based on sampled data $(X_{ih}_n)^n_{i=0}$, where $h_n downarrow 0$, focusing on cases... of either symmetric or completely skewed (one-sided) Levy density. First, the local asymptotic normality with always degenerate Fisher information matrix is obtained, so that the maximum likelihood estimation is inappropriate for joint estimation of all parameters involved. Second, supposing that either index or scale parameter is known, we obtain the uniform asymptotic normality of the maximum likelihood estimates and their asymptotic efficiency, where the resulting optimal convergence rates reveal that, as opposed to the Gaussian case, that $nh_n \rightarrow infty$ is not necessary for consistent estimation for all parameters.続きを見る

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レコードID 3391 査読無 MHF Preprint Series || 2006-18 || p1-13 http://www.math.kyushu-u.ac.jp/gakufu/ discrete sampling efficiency maximum likelihood estimation stable Levy process Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality 九州大学21世紀COEプログラム「機能数理学の構築と展開」 プレプリント 2009.04.22 2018.02.23