Sequential estimation based on conditional cost
Sequential estimation based on conditional cost
复制标题
基于条件成本的序贯估算
DOI：
10.1109/isit.2017.8006565
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Y. Mei
中科院分区：
文献类型：
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作者：
G. Moustakides;Tony Yaacoub;Y. Mei
我们考虑顺序框架下的参数估计问题。具体来说，我们假设 i.i.d.随机过程是按顺序观察的，其公共 pdf 具有必须估计的随机参数。我们感兴趣的是设计一个停止时间，该时间将决定何时是停止对过程进行采样的最佳时刻，以及一个估计器，该估计器将使用获取的样本来提供所需的估计。我们遵循半贝叶斯方法，将成本分配给一对（估计，真实参数），我们的目标是最小化平均样本大小，同时保证平均成本低于某个规定水平。在我们的分析中，我们采用了条件平均成本，这使得顺序估计问题得到了相当大的简化，否则在分析上是很困难的。我们将我们的结果应用于许多示例，并将我们的方法与最佳固定样本量以及现有的顺序方案进行比较。
We consider the problem of parameter estimation under a sequential framework. Specifically we assume that an i.i.d. random process is observed sequentially with its common pdf having a random parameter that must be estimated. We are interested in designing a stopping time that will decide when is the best moment to stop sampling the process and an estimator that will use the acquired samples in order to provide the desired estimate. We follow a semi-Bayesian approach where we assign cost to the pair (estimate, true parameter) and our goal is to minimize the average sample size guaranteeing at the same time an average cost below some prescribed level. For our analysis we adopt a conditional average cost which leads to a considerable simplification in the sequential estimation problem, otherwise known to be analytically intractable. We apply our results to a number of examples and compare our method with the optimum fixed sample size but also with existing sequential schemes.