Tail probabilities for the null distribution of scanning statistics
Tail probabilities for the null distribution of scanning statistics
复制标题
扫描统计数据零分布的尾部概率
DOI：
10.2307/3318574
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
B. Yakir
中科院分区：
文献类型：
--
作者：
D. Siegmund;B. Yakir
本文涉及扫描多维空间区域以检测噪声背景中的信号的统计量。背景被建模为来自自然参数的已知‘Null’值的指数族的独立观测，而信号由来自同一指数族的独立观测给出，但在空间域的特定分区上具有不同的参数值。主要结果是Pollak和Yakir方法的多维时间的扩展，该方法依赖于变点分析引起的度量的变化来近似估计似然比统计量的零分布。得到了大偏差近似和泊松近似。
This paper is concerned with statistics that scan a multidimensional spatial region to detect a signal against a noisy background. The background is modelled as independent observations from an exponential family of distributions with a known 'null' value of the natural parameter, while the signal is given by independent observations from the same exponential family, but with a different value of the parameter on a particular subregion of the spatial domain. The main result is an extension to multidimensional time of the method of Pollak and Yakir, which relies on a change of measure motivated by change-point analysis, to evaluate approximately the null distribution of the likelihood ratio statistic. Both large-deviation and Poisson approximations are obtained.