Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes
Hiroki Masuda
Source: Electron. J. Statist. Volume 4
(2010), 525-565.
Abstract
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 , where n denotes sample size and hn>0 the sampling mesh satisfying that hn→0 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
, 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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62M05
Keywords: Discrete-time sampling; Lévy process; Ornstein-Uhlenbeck process; self-weighted LAD estimation
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Permanent link to this document: http://projecteuclid.org/euclid.ejs/1276694114
Digital Object Identifier: doi:10.1214/10-EJS565
Mathematical Reviews number (MathSciNet): MR2660532
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