Mathematical Sciences: Leveraged Bootstrap

本研究的目的是研究一种新的重采样方法，称为杠杆引导。杠杆式Bootstrap使用各种类型的审查数据，包括正确审查数据，双重审查数据，区间审查数据等，促进了对非参数和半参数统计的广泛研究。该方法不依赖于将通常的完整数据统计扩展到不完整数据，具有简单、计算效率高、易于适用于各种不同类型截尾数据的统计推理问题的特点。本研究主要考虑以下问题：(1)杠杆自举在实践中如何应用；（ii）杠杆引导的效率；（三）与其他方法的比较。具体而言，研究者研究了杠杆自举在一些统计推断问题中的应用，如构建置信带和检验的经验似然方法，以及与多个统计模型相关的假设检验问题。在统计文献中，各种类型的截尾数据通常称为不完全数据。例如，一个死于心脏病的病人不可能再死于肺癌。在这种情况下，患者的肺癌生存时间是不完整的。近年来，在一些非常重要的临床试验中，如乳腺癌研究和艾滋病研究，都遇到了双重审查数据和间隔审查数据。对这类屏蔽数据的统计研究仍然普遍滞后于对正确屏蔽数据的统计研究。使用这些复杂类型的审查数据进行统计分析的主要困难在于，为完整数据开发的通常方法通常不能直接扩展到不完整数据，并且在某些情况下，通常的非参数自举可能会消耗相当多的计算时间。本研究旨在开发一种新的统计方法，该方法既准确，计算效率高，又易于适用于不同类型的屏蔽数据。＊＊＊

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. ***