通过深度条件生成学习对时间序列中的马尔科夫属性进行测试
Yunzhe Zhou1, Chengchun Shi2, Lexin Li1
1Division of Biostatistics, University of California at Berkeley, Berkeley, CA, USA.
概括
我们使用深度学习开发了一种新的非参数测试,用于高维时间序列中的马尔科夫属性. 这种方法准确地识别了马尔科夫属性,并确定了马尔科夫模型的顺序.
科学领域:
- 统计 统计 统计 统计
- 机器学习 机器学习
- 时间序列分析时间序列分析
背景情况:
- 马尔科夫属性是时间序列分析的基础,对于模拟顺序数据至关重要.
- 测试这个属性和确定马尔科夫模型的顺序是统计推理中的重要任务.
研究的目的:
- 为高维时间序列中马尔科夫属性的新型非参数测试提出建议.
- 为了扩展这个测试,对马尔科夫模型顺序的顺序确定.
- 为了建立测试性能的理论保证.
主要方法:
- 使用深度条件生成学习来估计条件密度函数.
- 开发一个双重可靠的测试统计数据,使用非参数估计和参数收率.
- 采用样品分割和交叉拟合,以提高测试一致性.
主要成果:
- 拟议的测试以非对称的方式控制了I型错误率.
- 测试表明功率接近一个,表明高检测能力.
- 理论分析为估计错误提供了明确的上限.
结论:
- 基于深度学习的非参数测试对高维时间序列有效.
- 该方法为马尔科夫属性测试和模型订单选择提供了一个强大的方法.
- 通过模拟和现实世界的数据应用来证明有效性.
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