Strong consistency of Bayesian estimator under discrete observation and unknown transition density
Strong consistency of Bayesian estimator under discrete observation and unknown transition density
复制标题
离散观测和未知转移密度下贝叶斯估计的强一致性
DOI：
10.1007/978-3-0348-0097-6_10
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
K. Yasuda
中科院分区：
文献类型：
--
作者：
A. Kohatsu-Higa;N. Vayatis;K. Yasuda
研究了离散平稳观测下贝叶斯参数估计方法的渐近性态。我们假设数据的转移密度是未知的，因此我们使用核密度估计方法对它进行近似，该方法应用于对产生观测的理论随机变量的近似值进行蒙特卡罗模拟。在这篇文章中，我们估计的理论估计，它假设的知识的过渡密度和它的近似，使用模拟之间的误差。我们证明了近似估计的强相合性，并找到了误差的阶。最重要的是，我们给出了一个参数调整的结果，它涉及的数据的数量，在近似过程中使用的时间步长的数量，Monte Carlo模拟的数量和核密度估计的带宽大小。
We consider the asymptotic behavior of a Bayesian parameter estimation method under discrete stationary observations. We suppose that the transition density of the data is unknown, and therefore we approximate it using a kernel density estimation method applied to the Monte Carlo simulations of approximations of the theoretical random variables generating the observations. In this article, we estimate the error between the theoretical estimator, which assumes the knowledge of the transition density and its approximation which uses the simulation. We prove the strong consistency of the approximated estimator and find the order of the error. Most importantly, we give a parameter tuning result which relates the number of data, the number of time-steps used in the approximation process, the number of the Monte Carlo simulations and the bandwidth size of the kernel density estimation.