Constant-Width Calibration Intervals for Linear Regression

Abstract

Calibration, in the sense of inverse regression, is widely used in measurement science and other applications. For univariate regression models, simultaneous calibration intervals enable one to construct confidence intervals for the unobserved values of the independent variable (x's) corresponding to an unlimited sequence (Y_n+1, Y_n+2, …) of future observations of the dependent variable. The intervals considered have the interpretation that if the initial training sample belongs to a specified set G of “good” outcomes, the conditional coverage probability for each future confidence interval will be at least the nominal value. The set G is constructed to occur with high probability. All methods for constructing calibration intervals currently in the literature are conservative in that they are obtained from simultaneous tolerance intervals for which the actual confidence level exceeds the nominal level. This work develops constant-width simultaneous tolerance intervals for which the bound on the nominal coverage probabilities is exact under normality. The resulting confidence intervals represent an attractive balance between efficiency and simplicity for linear calibration problems.

• Inverse Regression
• Simultaneous Tolerance Intervals

Additional information

Notes on contributors

Keith R. Eberhardt

Dr. Eberhardt is a Mathematical Statistician in the Statistical Engineering Division.

Robert W. Mee

Dr. Mee is an Associate Professor of Statistics.