论文标题
基于重要性抽样的有效较大偏差估计
Efficient large deviation estimation based on importance sampling
论文作者
论文摘要
我们提出了一个完整的框架，用于确定基于重要性采样的大偏差概率和速率函数的估计值的渐近（或对数）效率。该框架依赖于以下想法：在这种情况下的重要性采样完全以两个随机变量的关节大偏差为特征：可观察到的可观察到的较大的偏差概率和可能与原始过程相连的可能性因素（或Radon-nikodym衍生物）（或Radon-Nikodym衍生物）以及在重要性采样中使用的原始过程。我们使用此框架恢复了有关指数倾斜的渐近效率的已知结果，并获得了新的必要条件，以使一般过程的一般变化渐近地效率。这使我们能够为没有指数倾斜形式的随机变量的样本平均值构建有效估计器的新示例。提出了涉及马尔可夫链和扩散的其他例子，以说明我们的结果。
We present a complete framework for determining the asymptotic (or logarithmic) efficiency of estimators of large deviation probabilities and rate functions based on importance sampling. The framework relies on the idea that importance sampling in that context is fully characterized by the joint large deviations of two random variables: the observable defining the large deviation probability of interest and the likelihood factor (or Radon-Nikodym derivative) connecting the original process and the modified process used in importance sampling. We recover with this framework known results about the asymptotic efficiency of the exponential tilting and obtain new necessary and sufficient conditions for a general change of process to be asymptotically efficient. This allows us to construct new examples of efficient estimators for sample means of random variables that do not have the exponential tilting form. Other examples involving Markov chains and diffusions are presented to illustrate our results.
