The information domain confidence intervals in univariate linear calibration

Abstract

We consider the confidence interval for the univariate linear calibration, where a response variable is related to an explanatory variable by a simple linear model, and the observations of the response variable and known values of the explanatory variable are used to make inferences on a single unknown value of the explanatory variable. Since the univariate linear calibration suffers from a problem of local unidentifiability, which results in the confidence coefficient of every confidence interval with finite length being zero, we propose new confidence intervals in terms of information domain, which are verified to be $1-\alpha$ confidence intervals for a specified range of the interesting parameter. The proposed intervals are numerically compared with two existing methods, and simulations show that our confidence intervals have good behavior in the coverage probability and the expected length. We also illustrate the results using an example.

KEYWORDS:

• Coverage probability
• Expected length
• The information domain confidence interval
• Univariate linear calibration

Additional information

Funding

We are grateful to the reviewer for the valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China under Grant (No. 11471035) and Beijing Education Committee Science And Technology Plan General Project under Grant (No. KM201810009013).