论文标题
用于误指定的ErgodicLévy驱动的随机微分方程模型的引导程序方法
Bootstrap method for misspecified ergodic Lévy driven stochastic differential equation models
论文作者
论文摘要
在本文中，我们认为可能误指出的随机微分方程方程模型是由Lévy过程驱动的。不管驱动噪声是否为高斯，高斯准样品估计器都可以估计漂移和尺度系数中未知参数。但是，在误指定的情况下，估计值的渐近分布因校正错误指定偏差而有所不同，并且在正确指定的情况下提出的渐近方差的一致估计器可能会失去理论上的有效性。作为其解决方案之一，我们提出了一种近似渐近分布的自举方法。我们表明，在正确指定的情况和误指定的情况下，理论上的引导方法在不假定驾驶噪声的精确分布的情况下起作用。
In this paper, we consider possibly misspecified stochastic differential equation models driven by Lévy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, in the misspecified case, the asymptotic distribution of the estimator varies by the correction of the misspecification bias, and consistent estimators for the asymptotic variance proposed in the correctly specified case may lose theoretical validity. As one of its solutions, we propose a bootstrap method for approximating the asymptotic distribution. We show that our bootstrap method theoretically works in both correctly specified case and misspecified case without assuming the precise distribution of the driving noise.
