Corrected Brownian Approximations and Hybrid Bootstrap Applications

修正的布朗近似和混合自举应用

• 批准号: 0706771
• 负责人: Robert Keener
• 金额: $ 15万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706771&HistoricalAwards=false
• 关键词: Corrected; Brownian; Approximations; Hybrid; Bootstrap

Brownian motion approximations have been developed to estimate probabilities and expectations that arise in boundary crossing problems in discrete time. The proposed research derives correction terms to improve the accuracy of these Brownian approximations in various settings. The hybrid bootstrap is a new resampling method used to set confidence intervals. It is particularly relevant and appropriate when an experiment provides limited information about the parameter of interest, but substantial information about nuisance parameters. Three applications are considered: estimating the signal in a signal plus noise Poisson model of interest in high energy physics; estimating the location of a quantitative trait loci on a strand of DNA with data from a back-cross or inter-cross design; and estimating new parameters after sequential change point detection.Two different topics are considered for this project. The first concerns Brownian approximations. The specific goal is to derive correction terms to improve these approximations for a class of boundary crossing problems in discrete time. Brownian and diffusion approximations have been a major tool in stochastic modeling, with applications to diverse areas including sequential analysis in statistics, queuing theory for industrial and networking applications, and options pricing in finance. New methods to improve the accuracy these approximations should have broad value. The other topic concerns the hybrid bootstrap approach to interval estimation. Bootstrap methods in statistics use computer simulation to help a researcher assess the precision of an estimator. Hybrid bootstrapping is a modern variant of this approach which is particularly relevant in situations where the experiment provides limited information about the parameter of interest. Three specific applications are being studied. The first concerns experiments in physics in which a new particle or phenomenon, if present, will increase the rate of events, counted in the course of the experiment. A second application concerns modern genetics, trying to estimate locations for loci on a strand of DNA associated with a quantitative trait of interest. The final application arises in situations where a process of interest is monitored to detect changes. Industrial processes are often tracked since changes are often associated with production problems that should be noted and fixed as soon as possible to improve quality and output. Networks are often monitored for similar reasons, and financial series may be monitored for a variety of reasons. The hybrid bootstrap should be useful for new parameters describing process evolution after the change point.

布朗运动近似已经被开发来估计在离散时间中的边界交叉问题中出现的概率和期望。 拟议的研究推导出校正项，以提高这些布朗近似在各种设置的准确性。 混合自举法是一种新的确定置信区间的方法。当实验提供关于感兴趣的参数的有限信息，但关于讨厌的参数的大量信息时，它特别相关和适当。 考虑三种应用：估计高能物理中感兴趣的信号加噪声泊松模型中的信号;利用回交或互交设计的数据估计DNA链上数量性状位点的位置;以及估计序列变点检测后的新参数。第一个是布朗近似。具体的目标是获得修正项，以改善这些近似的一类边界跨越问题的离散时间。布朗近似和扩散近似一直是随机建模中的主要工具，应用于不同领域，包括统计中的序列分析，工业和网络应用的排队论，以及金融中的期权定价。提高这些近似精度的新方法具有广泛的应用价值。另一个主题是关于区间估计的混合Bootstrap方法。 统计学中的Bootstrap方法使用计算机模拟来帮助研究人员评估估计量的精度。混合自举是这种方法的现代变体，在实验提供有关感兴趣参数的有限信息的情况下特别相关。 目前正在研究三种具体应用。第一种是物理学实验，其中一个新的粒子或现象，如果存在，将增加事件的速率，在实验过程中计数。第二个应用涉及现代遗传学，试图估计与感兴趣的数量性状相关的DNA链上基因座的位置。最后一个应用程序出现的情况下，感兴趣的过程进行监测，以检测变化。工业过程经常被跟踪，因为变化往往与生产问题有关，应尽快注意和解决这些问题，以提高质量和产量。网络经常出于类似的原因受到监测，金融系列可能出于各种原因受到监测。混合引导应该是有用的新参数描述后的变化点的过程演变。