英文标题：
《A Second Order Cumulant Spectrum Test That a Stochastic Process is
Strictly Stationary and a Step Toward a Test for Graph Signal Strict
Stationarity》
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作者：
Denisa Roberts and Douglas Patterson
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最新提交年份：
2020
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英文摘要：
This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window averaged sample estimate of the second order cumulant spectrum to build a test statistic with an asymptotic complex standard normal distribution. We derive the test statistic, study the properties of the test and demonstrate its application using 137Cs gamma ray decay data. Future areas of research include testing for strict stationarity of graph signals, with applications in learning convolutional neural networks on graphs, denoising, and inpainting.
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中文摘要：
本文在频域上对离散时间随机过程的严格平稳性零假设进行了统计检验。当零假设成立时，主域中所有离散傅里叶频率对的二阶累积量谱均为零。该检验使用二阶累积量谱的窗口平均样本估计来建立具有渐近复标准正态分布的检验统计量。我们推导了检验统计量，研究了检验的性质，并用137Csγ射线衰变数据演示了其应用。未来的研究领域包括测试图形信号的严格平稳性，以及在图形上学习卷积神经网络、去噪和修复方面的应用。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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