Bootstrap Methods And Their Applications

Bootstrap methods are important ways to evaluate and improve the accuracyof statistics in statistical inference. Since Efron presented for the first time, theirtheoretical system developed and improved in continuous. The Bootstrap methodsare extensively applied in all fields. For example, financial, medical, military, foreigntrade, finance, biomedicine and so on. In this thesis, we made a comprehensivesummary of the bootstrap methods, applications of three methods for the estimateof confidence intervals in the calculation of VaR, and the improvement of bootstrapmethods.In the first chapter, the theoretical research background, the history and currentresearch status of bootstrap methods have been introduced. Then the main researchresults of this thesis have been given.In the second chapter, we introduced the basic ideas, the main principles andaccuracy, as well as the advantages and disadvantages of bootstrap methods.In the third chapter, we given a comprehensive summary of the bootstrap esti-mate of standard error, permutation-test and regression models.In the fourth chapter, we studied the bootstrap-t, the bootstrap percentiles andthe BCa confidence intervals.In the fifth chapter, we given the definition and calculation methods of valueat risk (VaR). Which we compared with the bootstrap-t, the bootstrap percentilesand the BCa confidence intervals. We obtained the result is the bootstrap-t, thebootstrap percentiles and the BCa confidence intervals are superior to the traditionalmethods of calculating VaR.In the sixth chapter, we given an improvement over the bootstrap methodsdefects.