AI 中文总结
本文针对平稳噪声中模型阶数选择问题，提出带随机网格抖动的差分逐步下降阈值算法，可实现渐近精确阶数恢复且鲁棒性强。
AI 中文摘要
本文研究平稳噪声中的模型阶数选择问题。单阈值检测对极端噪声偏移很敏感，尤其是当降低检测阈值以捕获弱确定性分量时。为增强单阈值检测，我们提出差分逐步下降阈值算法，该算法使用阈值网格；为克服网格评估导致的阈值网格错位误差，我们采用随机网格抖动。利用极值理论，我们证明了噪声极值的聚类特性，所提算法的停止规则可检测该聚类并终止算法以防止虚警。通过对阈值网格错位误差进行解析界定，我们证明该算法在0-1损失函数下可实现渐近精确阶数恢复，且即使原始单阈值算法的检测阈值被降低或出现极端噪声偏移，该算法仍保持鲁棒性。
英文摘要
This paper studies the problem of model order selection in stationary noise. Single-threshold detection is sensitive to extreme noise excursions, particularly when the detection threshold is lowered to capture weak deterministic components. To augment single-threshold detection, we propose a differential step-down thresholding algorithm. We use a threshold grid in this algorithm. To overcome the threshold grid misalignment error induced by grid evaluation, we utilize randomized grid dithering. Using extreme value theory, we show the clustering of the noise extrema. The stopping rule of the proposed algorithm detects this clustering and stops the algorithm to prevent false alarms. By analytically bounding the threshold grid misalignment error, we prove that our algorithm achieves asymptotic exact order recovery under the 0-1 loss function. Moreover, the proposed algorithm remains robust even if the detection threshold in the original single-threshold algorithm is lowered or extreme noise excursions occur.
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