Research On Confidence Interval Based On Bootstrap Method

The confidence interval shows the degree to which the true value of the parameter of interest falls around the measurement result,and gives the confidence degree of the measured value of the parameter of interest.The confidence interval is an important direction in statistical inference,because estimating the confidence interval is a prerequisite for our prediction.Interval estimation methods are also different for different statistical models.In many areas,Bootstrap become a kind of effective method of data processing,in many cases,the confidence interval of parameters of interest in the model is difficult to build,in order to solve this problem,this article is based on a class of Bootstrap confidence interval estimation method,rebuilding the bay leaf,Bootstrap confidence interval,respectively in the linear regression model and Bootstrap parameter estimation method of hierarchical linear regression model,and do the Monte Carlo simulation comparison and empirical analysis,comparative analysis the advantages and disadvantages of several methods.Bootstrap general estimation problem are introduced first,and then on the basis of a new class of confidence interval,in combination with Bootstrap method,construct Bootstrap confidence interval and bay leaf,Bootstrap confidence interval,Monte Carlo simulation results show that the bay leaf,Bootstrap method and Bootstrap method can better guarantee coverage in the name of the confidence level,bay leaf,Bootstrap method at the same time of guarantee coverage,higher stability than Bootstrap method;However,the classical method has a low coverage rate with a generally small sample size,and the average interval length is too long and more unstable.Considering the excellent performance of bayes Bootstrap confidence interval,it is recommended to use bayes Bootstrap as a good estimation method in practice.Secondly,a special error variance Bootstrap estimation method is proposed to estimate the parameters of interest in linear models.Under certain assumptions and through monte carlo simulation,it is concluded that Bootstrap estimation method and Bootstrap estimation method of error variance are better than traditional estimation method in the case of small sample size.When the sample size is large,the error variance Bootstrap and Bootstrap method are slightly better than the least square estimation method in accuracy.Then,Monte Carlo simulation is used to compare the performance of traditional statistical method and parameter Bootstrap in hierarchical linear model.The results show that the Bootstrap method is superior to the traditional statistical method on the basis of the hierarchical linear model and in the case of small samples.Finally,Case Analysis was carried out to explain Bootstrap by using two subsets respectively.One was used to analyze and predict population aging,and the other was used to predict coronavirus.