Exact Confidence Intervals for Parameters in Linear Models With Parameter Constraints
- Resource Type
- Conference
- Authors
- Witkovsky, Viktor; Wimmer, Gejza
- Source
- 2021 13th International Conference on Measurement Measurement, 2021 13th International Conference on. :22-25 May, 2021
- Subject
- Bioengineering
Communication, Networking and Broadcast Technologies
Engineered Materials, Dielectrics and Plasmas
Fields, Waves and Electromagnetics
General Topics for Engineers
Photonics and Electrooptics
Power, Energy and Industry Applications
Signal Processing and Analysis
Uncertainty
Systematics
Computational modeling
Measurement uncertainty
Linear regression
Metrology
Probability distribution
Linear Regression Model
Parameter Constraints
Best Linear Unbiased Estimator
Exact Distribution
Confidence Interval
Characteristic Function Approach (CFA)
- Language
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.