时间序列滤波中的置信集
Confidence Sets in Time-Series Filtering
摘要：
研究了有限字母平稳遍历时间序列的滤波问题。提出了一种用于构造（未知）信号的置信集的方法，使得所得到的集合具有以下性质：首先，它包括具有概率$γ$的未知信号，其中$γ$是提供给滤波器的参数。其次，置信集的大小以渐近等于给定数据的信号的条件熵的速率呈指数增长。此外，它表明，该速率是最佳的。
英文摘要：
The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties: First, it includes the unknown signal with probability $γ$, where $γ$ is a parameter supplied to the filter. Second, the size of the confidence sets grows exponentially with the rate that is asymptotically equal to the conditional entropy of the signal given the data. Moreover, it is shown that this rate is optimal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
