标题： 去偏连续时间非线性自回归模型 显示英文标题

标题： Debiasing Continuous-time Nonlinear Autoregressions

摘要： 我们研究了如何识别一类由常微分方程定义且关于未知参数仿射的连续时间非线性系统。 我们定义了一种渐近一致性的概念，即$(n, h) \to (\infty, 0)$，并通过一个直接方法族实现了这一目标，其中第一步是对含噪时间序列求导，第二步是嵌入式的线性估计器。 第一步，求导，是非参数统计局部多项式回归技术在信号处理中的应用。 第二步，广义线性回归，可以通过最小二乘估计实现一致性，但我们提出了两种新的偏差校正方法，以提高有限样本大小$h$的准确性。 这些方法显著扩展了可以通过直接方法一致估计的连续时间系统的类别。 显示英文摘要

摘要： We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it using a family of direct methods where the first step is differentiating a noisy time series and the second step is a plug-in linear estimator. The first step, differentiation, is a signal processing adaptation of the nonparametric statistical technique of local polynomial regression. The second step, generalized linear regression, can be consistent using a least squares estimator, but we demonstrate two novel bias corrections that improve the accuracy for finite $h$. These methods significantly broaden the class of continuous-time systems that can be consistently estimated by direct methods.