与一阶自回归过程相关的Durbin-Watson统计量的中偏差
Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process
摘要：
本文的目的是研究与稳定的一阶自回归过程相关的Durbin-Watson统计量的中等偏差，其中驱动噪声也由一阶自回归过程给出。首先，我们建立了一个适度的偏差原则的最小二乘估计的未知参数的自回归过程，以及与驱动噪声的串行相关估计。它使我们能够提供一个温和的偏差原则的Durbin-Watson统计在简单的情况下，驱动噪声是正态分布的，在更一般的情况下，驱动噪声满足限制较少的陈勒杜型条件。
英文摘要：
The purpose of this paper is to investigate moderate deviations for the Durbin-Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate deviation principle for the Durbin-Watson statistic in the easy case where the driven noise is normally distributed and in the more general case where the driven noise satisfies a less restrictive Chen-Ledoux type condition.
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