摘要：We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter a1 in a non-degenerate diffusion coefficient and a parameter a2 in the drift term. The second component has a drift term parameterized by a3 and no diffusion term. Asymptotic normality is proved in two different situations for an adaptive estimator for a3 with some initial estimators for (a1,a2), and an adaptive one-step estimator for (a1,a2,a3) with some initial estimators for them. Our estimators incorporate information of the increments of both components. Thanks to this construction, the asymptotic variance of the estimators for a1 is smaller than the standard one based only on the first component. The convergence of the estimators for a3 is much faster than the other parameters. The resulting asymptotic variance is smaller than that of an estimator only using the increments of the second component.
