Construction Of Monte Carlo And Conditional Monte Carlo Simultaneous Confidence Bands And Comparisons

The construction of confidence band is an important inference research problem in theoret-ical statistics.Compared with common confidence interval,confidence band not only has better multivariate statistical significance,but also has good application prospect.In the development process of confidence band research,a series of achievements represented by Scheffe,Naiman and others have appeared,among which Liu at el.^[1]proposed the construction process of ac-curate confidence band based on Monte Carlo simulation,Trotter&Tukey^[2]proposed the idea of building confidence band based on conditional Monte Carlo simulation.It was popularized by Hammersley^[3].In this paper,multiple linear regression and polynomial regression models are selected to derive the formula of confidence band parameters based on Monte Carlo and conditional Monte Carlo,and then the hyperbolic confidence bands and constant width confidence band are constructed.Then,the critical value and confidence band coverage probability are used as evaluation indexes to design simulation experiments.The performance of the two methods under different data distributions and parameter combinations is comprehensively compared to improve the conclusion.