Bootstrap方法的歷史發(fā)展及其在金融風險管理和藥物動力學中的應用.pdf

1、華中科技大學碩士學位論文Bootstrap方法的歷史發(fā)展及其在金融風險管理和藥物動力學中的應用姓名：曾翀申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：萬建平20090511華 中 科 技 大 學 碩 士 學 位 論 文 華 中 科 技 大 學 碩 士 學 位 論 文 IIAbstract The bootstrap methods were raised by Efron, a scholar from Stanford Univ

2、ersity, in 1979. In the past 30 years, bootstrap methods have been developed and employed in many fields. This theory and methodology composed of IID bootstrap and bootstrap for dependent data, among which the first dire

3、ction 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 historical development and so

4、me frontiers of the bootstrap theory, such as bootstrap for Markov process, bootstrap for long-range dependence and bootstrap for spatial data. Bootstrap methods were carried out in two fields of application in this pape

5、r. Firstly, in financial risk management studies, confidence intervals for VaR are generally ignored, so we described several approaches to bootstrap confidence intervals for VaR, and comparisons among these approaches a

6、re made. Secondly, in population pharmacokinetics studies, confidence intervals for population pharmacokinetics parameters are generally estimated by assuming the asymptotic normality, which is a large-sample property, t

7、hat 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 sample sizes of actual tr

8、ials are often not large enough for assuming the asymptotic normality and that the asymptotic confidence intervals underestimate the uncertainties of the estimates of population pharmacokinetics parameters. As an alterna

9、tive to the asymptotic normality approach, we can employ a bootstrap approach. This paper proposes a bootstrap percentile approach for constructing confidence intervals for population pharmacokinetics parameters. Compari