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2010 Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes
Hiroki Masuda
Electron. J. Statist. 4: 525-565 (2010). DOI: 10.1214/10-EJS565


We consider drift estimation of a discretely observed Ornstein-Uhlenbeck process driven by a possibly heavy-tailed symmetric Lévy process with positive activity index β. Under an infill and large-time sampling design, we first establish an asymptotic normality of a self-weighted least absolute deviation estimator with the rate of convergence being $\sqrt{n}h_{n}^{1-1/\beta}$, where n denotes sample size and hn>0 the sampling mesh satisfying that hn0 and nhn. This implies that the rate of convergence is determined by the most active part of the driving Lévy process; the presence of a driving Wiener part leads to $\sqrt{nh_{n}}$, which is familiar in the context of asymptotically efficient estimation of diffusions with compound Poisson jumps, while a pure-jump driving Lévy process leads to a faster one. Also discussed is how to construct corresponding asymptotic confidence regions without full specification of the driving Lévy process. Second, by means of a polynomial type large deviation inequality we derive convergence of moments of our estimator under additional conditions.


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Hiroki Masuda. "Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes." Electron. J. Statist. 4 525 - 565, 2010.


Published: 2010
First available in Project Euclid: 16 June 2010

zbMATH: 1329.62364
MathSciNet: MR2660532
Digital Object Identifier: 10.1214/10-EJS565

Primary: 62M05

Keywords: Discrete-time sampling , Lévy process , Ornstein-Uhlenbeck process , self-weighted LAD estimation

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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