Theory of Probability and Mathematical Statistics
Non-adaptive estimation for degenerate diffusion processes
Arnaud Gloter and Nakahiro Yoshida
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Abstract: We consider a degenerate system of stochastic differential equations. The first component of the system has a parameter θ1 in a non-degenerate diffusion coefficient and a parameter θ2 in the drift term. The second component has a drift term with a parameter and no diffusion term. Parametric estimation of the degenerate diffusion system is discussed under a sampling scheme. We investigate the asymptotic behavior of the joint quasi-maximum likelihood estimator for (θ1,θ2,θ3). The estimation scheme is non-adaptive. The estimator incorporates information of the increments of both components, and under this construction, we show that the asymptotic variance of the estimator for θ1 is smaller than the one for standard estimator based on the first component only, and that the convergence of the estimator for θ2 is much faster than for the other parameters. By simulation studies, we compare the performance of the joint quasi-maximum likelihood estimator with the adaptive and one-step estimators investigated in Gloter and Yoshida [Electron. J. Statist 15 (2021), no. 1, 1424–1472].
Keywords: Degenerate diffusion, quasi-maximum likelihood estimator
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