Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes

作者：Masuda Hiroki^*

来源：Electronic Journal of Statistics, 2010, 4: 525-565.

DOI：10.1214/10-EJS565

• Discrete-time sampling
• Levy process
• Ornstein-Uhlenbeck process
• self-weighted LAD estimation

We consider drift, estimation of a discretely observed Ornstein-Uhlenbeck process driven by a possibly heavy-tailed symmetric Levy process with positive activity index beta. 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 root nh(n)(1-1/beta) where n denotes sample size and h(n) > 0 the sampling mesh satisfying that h(n) -> 0 and nh(n) -> infinity. This implies that the rate of convergence is determined by the most active part of the driving Levy process; the presence of a driving Wiener part leads to root nh(n), which is familiar in the context of asymptotically efficient estimation of diffusions with compound Poisson jumps, while a pure-jump driving Levy process leads to a faster one. Also discussed is how to construct corresponding asymptotic confidence regions without full specification of the driving Levy process. Second, by means of a polynomial type large deviation inequality we derive convergence of moments of our estimator under a mal conditions.

• 出版日期2010