Mathematical Sciences: Expanison and Likelihood Methods forMartingales and Martingale Inference

数学科学：鞅和鞅推理的展开和似然方法

• 批准号: 9305601
• 负责人: Per Mykland
• 金额: $ 6.7万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305601&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Expanison; Likelihood; Methods

This research is concerned with inference for longitudinal data, such as of survival analysis and time series type. Tests and confidence intervals in such problems are typically based on the asymptotic behavior of martingales. This project will focus on more accurate ways of setting critical points in such inference. One approach to this problem is to transform the martingales to create statistics more accurately approximated by the asymptotic distribution. Another approach is to look for better approximations to the law of the martingale, via Edgeworth or saddlepoint expansions, or bootstrapping. The research is intended to improve the way statisticians interpret data from processes that evolve over time. Main cases are (1) long term medical data, where patients are followed over a period of time, and (2) economic data. These quite different types of settings can be studied with a relatively unified technology, which relates to the theory of fair games. Substantial gains in how data are interpreted can be obtained by further exploiting this connection.

本研究涉及纵向推理 数据，例如生存分析和时间序列类型。 测试 在这些问题中的置信区间通常基于 鞅的渐近行为 该项目将重点 更准确地设定临界点， 推论 解决这个问题的一种方法是将 鞅来创建更准确的统计近似 渐近分布 另一种方法是寻找 更好地逼近鞅定律，通过Edgeworth 或鞍点展开或自举。 这项研究旨在改善统计学家 从随时间演变的过程中解释数据。 主要情况 是（1）长期的医疗数据，其中患者被随访 一段时间;（2）经济数据。 这些完全不同的 类型的设置可以与一个相对统一的研究 技术，这涉及到公平游戏的理论。 通过以下方式，可以在如何解释数据方面获得实质性的收益 进一步利用这种联系。