Discriminant analysis based on binary time series
Discriminant analysis based on binary time series
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DOI：
10.1007/s00184-019-00746-1
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发表时间：
2019-10
期刊：
影响因子：
0.7
通讯作者：
Yuichi Goto;M. Taniguchi
中科院分区：
文献类型：
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作者：
Yuichi Goto;M. Taniguchi
二进制时间序列可以从潜在的潜在过程中得到。本文考虑了椭球α混合严格平稳过程，讨论了判别分析，提出了一种基于二进制时间序列的分类方法。假设观测是由时间序列产生的，该时间序列属于由不同谱描述的两个类别中的一个。我们提出了一种高概率地归入正确类别的方法。首先，我们将证明，当观测次数趋于无穷大时，错误分类概率趋于零，即我们的判别方法的一致性。进一步，我们估计了当两个类别是连续的时的渐近错误分类概率。最后，我们证明了基于二进制时间序列的分类方法在过程受到离群点污染时具有良好的稳健性，即我们的分类方法对离群点不敏感。然而，基于平滑周期图的经典方法对孤立点比较敏感。我们还处理了一个实际案例，其中这两个类别是根据训练样本估计的。对于一个心电数据集，我们检验了当观测数据被异常值污染时，我们方法的稳健性。
Binary time series can be derived from an underlying latent process. In this paper, we consider an ellipsoidal alpha mixing strictly stationary process and discuss the discriminant analysis and propose a classification method based on binary time series. Assume that the observations are generated by time series which belongs to one of two categories described by different spectra. We propose a method to classify into the correct category with high probability. First, we will show that the misclassification probability tends to zero when the number of observation tends to infinity, that is, the consistency of our discrimination method. Further, we evaluate the asymptotic misclassification probability when the two categories are contiguous. Finally, we show that our classification method based on binary time series has good robustness properties when the process is contaminated by an outlier, that is, our classification method is insensitive to the outlier. However, the classical method based on smoothed periodogram is sensitive to outliers. We also deal with a practical case where the two categories are estimated from the training samples. For an electrocardiogram data set, we examine the robustness of our method when observations are contaminated with an outlier.