Threshold Estimation for Stochastic Processes with Small Noise
Threshold Estimation for Stochastic Processes with Small Noise
复制标题
小噪声随机过程的阈值估计
DOI：
10.1111/sjos.12287
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发表时间：
2017
影响因子：
1
通讯作者：
Shimizu Yasutaka
中科院分区：
文献类型：
--
作者：
村上佑希;山本良太;西村憲明;上薗拓郎;山岸義和;Shimizu Yasutaka
考虑一个过程满足一个具有未知漂移参数的随机微分方程，并假设给出离散观测。众所周知，当噪声过程有跳跃时，简单的最小二乘估计(LSE)在有限样本下的大标准差意义上是一致的，但在数值上是不稳定的。我们提出了一个过滤器来从数据中剔除大的冲击，并从过滤器选择的数据中构造相同的最小二乘估计。该估计器可以渐近等价于通常的最小二乘估计，其渐近分布强烈依赖于噪声过程。然而，在数值研究中，在一个适当选择滤波器的例子中，它看起来是渐近正常的，并且噪声是一个L过程。在某些有限的假设下，我们将试图从数学上证明这一现象的合理性。
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.