Bootstrap方法历史发展及其在金融风险管理和药物动力学中应用.pdf

华 中 科 技 大 学 硕 士 学 位 论 文 I 摘要 1979 年美国斯坦福大学的学者 Efron 第一次系统地提出了 Bootstrap 方法。 30 年间, Bootstrap 理论不断发展和丰富,应用领域不断扩大。 Bootstrap 理论体系主要包含以下两个方面:基于独立同分步数据和基于具有相依结构数据的 Bootstrap ,其中于独立同分布数据的 Bootstrap 是整个 Bootstrap 理论体系的核心。本文简介了依和空间数据的 Bootstrap 理论。本文将 Bootstrap 方法在两个领域中进行了应用。 1 )针对传统 VaR 计算中,人们忽视了 VaR 的区间估计,本文提出了运用自助法构建 VaR 的置信区间的方法,并且比较了几种方法各自的特点。 2 )在以往的药物动力学研究中,研究者通过假设群体 PK 参数估计具有渐近容量足够大时,参数估计才具有这种性质。但是,在实际的临床试验中,由于各种客观因素的限制,样本容量往往是有限的。因此,我们对群体 PK 参数估计的渐近正态性假设的合理性提出质疑。本文运用自助百分位法验证了在实际临床实验中,由于通常样本容量不够大,对群体 PK 参数估计的渐近正态性假设是不合理的,由渐近正态性假设得出的置信区间低估了群体 PK 参数估计的不稳定性。关键词: 自助法;参数估计; VaR ;群体 PK 参数; NONMEN 华 中 科 技 大 学 硕 士 学 位 论 文 II Abstract The bootstrap methods were raised by Efron, a scholar from Stanford University, in 1979. In the past 30 years, bootstrap methods ha ve been developed and employed in many fields. This theory and p osed of IID bootstrap and bootstrap for dependent data, among which the first direction is the most fundamental, and the latter one includes model-based bootstrap, block bootstrap, transformation-based bootstrap and sieve bootstrap. This paper gives an introduction of the historic al development and some frontiers of the bootstrap th eory, such as bootstrap for Markov process, bootstrap for long-range dependence and bootstrap for spatial data. Bootstrap methods were carried out in two fiel ds of application in this paper. Firstly, in financial risk management studies, confiden ce intervals for VaR are generally ignored, so we described several approaches to bootstrap confidence inte rvals for VaR, and comparisons among these approaches are ma de. Secondly, in population ics studies, confidence intervals for population pha ics parameters are generally estimated by assuming the asymptotic normality, which is a large-sample property, that is, a property which holds for case where sample sizes are large enough. In actual clinical trials, however, sample sizes are limited and not so large in general. We hence suspected that the s