Research On Statistical Inference Of Multivariate-Univariate Linear Calibration Model

Linear calibration model is a kind of statistical model under the background of measurement,it has important theoretical and application value.In this dissertation,we focus on the statistical inference for the multivariate-univariate linear calibration,a multivariate-univariate linear calibration model based on calibration data to infer a single unknown value of an explanatory variable.Firstly,we apply the generalized inference to the calibration problem,and take the generalized p-value as the test statistic to develop two new p-values for one-sided hypothesis testing,which we refer to as the posterior predictive and parametric bootstrap p-value and the posterior predictive pvalue.The behavior of the two new p-values are numerically compared with the generalized p-value in frequency distribution,and the two p-values are compared with the parametric bootstrap method in error-I rate and power.Simulations show that the two new p-values are superior than the parametric bootstrap method.Secondly,we compare three types of test statistics under two posterior prediction methods in the error-I rate and power.Next,the better performing test statistics are used as the pivot statistics in the interval estimation.The simulation results show that the two test statistics under the posterior prediction method perform better.Finally,the better performance of test statistics are used in the example and compared with the parametric bootstrap method,the results are better than existing methods.The results show that the posterior prediction p-values and the test statistics under the posterior prediction method perform well,and it is very practical in this dissertation.