论文标题
退化扩散过程的自适应和非自适应估计
Adaptive and non-adaptive estimation for degenerate diffusion processes
论文作者
论文摘要
我们讨论了从时间污染观察结果中退化扩散系统的参数估计。退化扩散系统的第一个组件在非脱位扩散系数中具有参数$θ_1$，并且在漂移项中具有参数$θ_2$。第二个组件的漂移项为$θ_3$，没有扩散项。 Asymptotic normality is proved in three different situations for an adaptive estimator for $θ_3$ with some initial estimators for ($θ_1$ , $θ_2$), an adaptive one-step estimator for ($θ_1$ , $θ_2$ , $θ_3$) with some initial estimators for them, and a joint quasi-maximum likelihood estimator for ($θ_1$ , $θ_2$，$θ_3$）没有任何初始估计器。我们的估计器包含了两个组件增量的信息。由于这种结构，$θ_1$的估计器的渐近方差小于仅基于第一个组件的标准差异。 $θ_3$的估计器的收敛速度比其他参数快得多。所得的渐近方差小于仅使用第二个组件的增量的估计器的方差。
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $θ_1$ in a non-degenerate diffusion coefficient and a parameter $θ_2$ in the drift term. The second component has a drift term parameterized by $θ_3$ and no diffusion term. Asymptotic normality is proved in three different situations for an adaptive estimator for $θ_3$ with some initial estimators for ($θ_1$ , $θ_2$), an adaptive one-step estimator for ($θ_1$ , $θ_2$ , $θ_3$) with some initial estimators for them, and a joint quasi-maximum likelihood estimator for ($θ_1$ , $θ_2$ , $θ_3$) without any initial estimator. Our estimators incorporate information of the increments of both components. Thanks to this construction, the asymptotic variance of the estimators for $θ_1$ is smaller than the standard one based only on the first component. The convergence of the estimators for $θ_3$ 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.
