Exact Confidence Intervals for Parameters in Linear Models With Parameter Constraints

We consider the exact distribution of the best linear unbiased estimator (BLUE) of a linear combination of the unknown model parameters in linear models with possible parameters constraints. Here, we present a method for computing the exact confidence intervals for the considered linear combinations of the model parameters under the assumption that the errors are linear combinations of independent random variables with known probability distributions. This is a typical situation in measurement and metrology. It is often necessary to consider systematic errors or uncertainties determined by Type B evaluation (i.e., based on expert knowledge). The proposed method for calculating the confidence intervals uses the characteristic function approach (CFA) and suitable algorithms for numerical inversion of the characteristic function.