Research On Interval Estimation Of Linear Calibration Models

Linear calibration models are a type of statistical model generated from measurement backgrounds,widely used in chemical experiments,biological measurements,and environmental monitoring.This article studies the interval estimation problem of univariate and multivariate-univariate linear calibration models,which constructs a linear calibration model based on known calibration data to infer a single unknown value of the independent variable.Firstly,the Fiducial method is used to construct a generalized confidence interval,and then the information domain is combined to modify the generalized confidence interval to obtain the modified generalized confidence interval.For the multivariate-univariate linear calibration model,the confidence interval of the posterior prediction distribution after information domain calibration is also given.Numerical simulation shows that when the nuisance parameter or norm of parameterβ₁ is small,the interval length of the information domain calibration confidence interval has significantly improved.For the univariate linear calibration model,both simulations and examples show that the modified generalized confidence interval in the information domain has good frequency performance.The simulation results of multivariate-univariate linear calibration show that when the sample size is small or slightly larger than the norm ofβ₁ at the same time,the confidence interval of the information domain calibration posterior prediction distribution has more advantages in frequency performance.When the sample size and norm ofβ₁ are both large,the length of the modified generalized confidence interval in the information domain is shorter.