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June 2013 Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency
Hiroki Masuda
Ann. Statist. 41(3): 1593-1641 (June 2013). DOI: 10.1214/13-AOS1121


This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a Lévy driven stochastic differential equation whose coefficients are known except for the finite-dimensional parameters to be estimated, where the diffusion coefficient may be degenerate or even null. We suppose that the process is discretely observed under the rapidly increasing experimental design with step size $h_{n}$. By means of the polynomial-type large deviation inequality, convergence of the corresponding statistical random fields is derived in a mighty mode, which especially leads to the asymptotic normality at rate $\sqrt{nh_{n}} $ for all the target parameters, and also to the convergence of their moments. As our Gaussian quasi-likelihood solely looks at the local-mean and local-covariance structures, efficiency loss would be large in some instances. Nevertheless, it has the practically important advantages: first, the computation of estimates does not require any fine tuning, and hence it is straightforward; second, the estimation procedure can be adopted without full specification of the Lévy measure.


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Hiroki Masuda. "Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency." Ann. Statist. 41 (3) 1593 - 1641, June 2013.


Published: June 2013
First available in Project Euclid: 1 August 2013

zbMATH: 1292.62124
MathSciNet: MR3113823
Digital Object Identifier: 10.1214/13-AOS1121

Primary: 62M05

Keywords: exponential ergodicity , Gaussian quasi-likelihood estimation , high-frequency sampling , Lévy driven stochastic differential equation , polynomial-type large deviation inequality

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 3 • June 2013
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