In this‐30 work we propose a model selection criterion to estimate the points of independence of a random vector, producing a decomposition of the vector distribution function into independent blocks. The method, based on a general estimator of the distribution function, can be applied for discrete or continuous random vectors, and for i.i.d. data or dependent time series. We prove the consistency of the approach under general conditions on the estimator of the distribution function and we show that the consistency holds for i.i.d. data and discrete time series with mixing conditions. We also propose an efficient algorithm to approximate the estimator and show the performance of the method on simulated data. We apply the method in a real dataset to estimate the distribution of the flow over several locations on a river, observed at different time points.

中文翻译：

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多元时间序列中的独立块识别

在这30项工作中，我们提出了一个模型选择标准来估计随机向量的独立点，从而将向量分布函数分解为独立的块。该方法基于分布函数的一般估计，可以应用于离散或连续随机向量，以及iid数据或相关时间序列。我们在分布函数的估计量上证明了在一般条件下该方法的一致性，并且表明该一致性对于混合条件下的iid数据和离散时间序列成立。我们还提出了一种有效的算法来近似估计器，并在仿真数据上显示了该方法的性能。我们将该方法应用于实际数据集中，以估算河流上多个位置的流量分布，