Mathematical Sciences: Leveraged Bootstrap

数学科学：利用 Bootstrap

• 批准号: 9626532
• 负责人: Jian-Jian Ren
• 金额: $ 6.3万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626532&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Leveraged; Bootstrap

DMS 96-26532 Ren The objective of this research is to investigate a new resampling method, called the Leveraged Bootstrap. The Leveraged Bootstrap facilitates research in a broad class of nonparametric and semiparametric statistics using various types of censored data, including right censored data, doubly censored data, interval censored data, etc.. This method does not depend on the extensions of the usual statistics for complete data to incomplete data, and is simple, computationally efficient and easily applicable to a wide of variety of statistical inference problems with different types of censored data. In this research, the following issues are considered: (i) how the leveraged bootstrap should be applied in practice; (ii) the efficiency of the leveraged bootstrap; (iii) comparison with other methods. Specifically, the investigator studies the application of the leveraged bootstrap in some statistical inference problems such as the empirical likelihood methods in constructing confidence bands and tests, and the hypothesis testing problems which are associated with several statistical models. %%% Various types of censored data are generally referred to as incomplete data in statistics literature. For instance, a patient who has died from heart disease cannot go on to die from lung cancer. In such a case, the survival time of lung cancer of the patient is incomplete. Recently, doubly censored data and interval censored data have been encountered in some very important clinical trials such as breast cancer research and AIDS research. The statistical research on these types of censored data still generally lags behind that on right censored data. The principle difficulties in statistical analysis using these complicated types of censored data are that the usual methods developed for complete data often do not have direct extensions to incomplete data, and that the usual nonparametric bootstrap can be quite computationally time consuming in certain cases. This research is to develop some new statistical methods which are accurate, computationally efficient and easily applicable for different types of censored data. ***

DMS 96-26532这项研究的目的是研究一种新的重采样方法，称为Leveraged Bootstrap。杠杆式的引导程序促进了使用各种审查的数据，包括右审查数据，双重审查数据，间隔审查的数据等，促进了一类广泛的非参数和半参数统计的研究。此方法不取决于该方法的扩展。完整的数据以使数据不完整，并且简单，计算上有效且易于适用于具有不同类型的审查数据的各种统计推断问题。在这项研究中，考虑了以下问题：（i）应如何在实践中应用杠杆式引导； （ii）杠杆引导的效率； （iii）与其他方法进行比较。具体而言，研究者研究了杠杆引导在某些统计推断问题中的应用，例如在构建置信带和测试中的经验可能性方法，以及与多种统计模型相关的假设测试问题。 %% %%各种各样的审查数据通常称为统计文献中的不完整数据。例如，死于心脏病的患者不能继续死于肺癌。在这种情况下，患者肺癌的生存时间不完整。 最近，在一些非常重要的临床试验（例如乳腺癌研究和艾滋病研究）中遇到了双重审查的数据和间隔审查的数据。对这些类型的审查数据的统计研究通常仍然落后于右审查数据。 使用这些复杂类型的审查数据的统计分析中的主要困难是，为完整数据开发的通常方法通常没有直接扩展数据以使数据不完整，并且通常在某些情况下，通常的非参数bootstrap可以在计算上很耗时。这项研究是为了开发一些新的统计方法，这些方法准确，计算上有效且易于适用于不同类型的审查数据。 ***