USING THE SMOOTHED BOOTSTRAP FOR STATISTICAL INFERENCE FOR MARKOV CHAINS
USING THE SMOOTHED BOOTSTRAP FOR STATISTICAL INFERENCE FOR MARKOV CHAINS
复制标题
使用平滑自举程序进行马尔可夫链的统计推断
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Polansky
中科院分区：
文献类型：
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作者：
A. Polansky
马尔可夫链为因缘随机变量提供了一种灵活的模型，在物理、环境科学和经济学等学科中都有应用。最近，自举法已被用于帮助开发基于从马尔可夫链观察到的实现的统计方法。自举法利用观测实现估计的马尔可夫链的转移概率矩阵估计具有未知转移概率矩阵的马尔可夫链的参数。不幸的是，当观测到的实现长度不够大时，估计的转移概率矩阵的性质往往与实际的转移概率矩阵的性质有很大的不同。这可能导致与自举估计相关的较大误差。本文提出了一种简单的多项式型平滑技术，可用于估计转移概率矩阵，以减轻这些困难。实证研究表明，平滑转移概率矩阵的使用可以提高马尔可夫链自举方法的可靠性。通过实例说明了该方法的实际应用。
Markov chains provide a flexible model for dependent random variables with applications in such disciplines as physics, environmental science and economics. Recently the bootstrap has been used to aid in the development of statistical methods based on observed realizations from Markov chains. The bootstrap method estimates parameters of the Markov chain with an unknown transition probability matrix with those from a Markov chain with a transition probability matrix estimated using the observed realization. Unfortunately, when the length of the observed realization is not sufficiently large, the properties of the estimated transition probability matrix are often very different from those of the actual transition probability matrix. This can lead to large errors associated with the bootstrap estimates. This paper presents simple multinomial type smoothing techniques that can be applied to the estimated transition probability matrix to alleviate some of these difficulties. It is demonstrated through empirical studies that the use of the smoothed transition probability matrix can increase the reliability of the bootstrap method for Markov chains. The practical use of the method is demonstrated through an example.