论文标题

使用二进制测量值的VAR估计器

VAR estimators using binary measurements

论文作者

Cros, Colin, Amblard, Pierre-Olivier, Manton, Jonathan H.

论文摘要

在本文中,引入了两种新型算法,以估算从1位测量值中估算高斯矢量自回旋(VAR)模型。它们基于修改的Yule-Walker方案以说明定量。标量案例以前已经研究过。从标量到向量情况的主要困难是如何估计VAR模型成对成分方差的比率。第一种方法通过要求定量为非对称来克服这一困难:VAR模型输出的每个组件被二进制“零”或二进制“一个”代替,具体取决于其值是否大于严格的正阈值。 VAR模型的不同组件可以具有不同的阈值。由于这些阈值的选择对性能有很大的影响,因此,第一种方法最适合在选择相应阈值之前每个时间序列的方差大致知道的应用。第二种方法不仅依赖于不仅对VAR模型的每个组件的对称定量,还取决于组件的成对差异。这些额外的测量值等于从最小的组件到最大组件的瞬时var模型输出的排名。这避免了选择阈值的需求,但需要其他硬件来对组件成对进行量化。数值模拟显示了这两个方案的效率。

In this paper, two novel algorithms to estimate a Gaussian Vector Autoregressive (VAR) model from 1-bit measurements are introduced. They are based on the Yule-Walker scheme modified to account for quantisation. The scalar case has been studied before. The main difficulty when going from the scalar to the vector case is how to estimate the ratios of the variances of pairwise components of the VAR model. The first method overcomes this difficulty by requiring the quantisation to be non-symmetric: each component of the VAR model output is replaced by a binary "zero" or a binary "one" depending on whether its value is greater than a strictly positive threshold. Different components of the VAR model can have different thresholds. As the choice of these thresholds has a strong influence on the performance, this first method is best suited for applications where the variance of each time series is approximately known prior to choosing the corresponding threshold. The second method relies instead on symmetric quantisations of not only each component of the VAR model but also on the pairwise differences of the components. These additional measurements are equivalent to a ranking of the instantaneous VAR model output, from the smallest component to the largest component. This avoids the need for choosing thresholds but requires additional hardware for quantising the components in pairs. Numerical simulations show the efficiency of both schemes.

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