CONSTANT-WIDTH CALIBRATION INTERVALS FOR LINEAR-REGRESSION

Calibration, in the sense of inverse regression, is widely used in mea surement science and other applications. For univariate regression mod els, simultaneous calibration intervals enable one to construct confid ence intervals for the unobserved values of the independent Variable ( x's) corresponding to an unlimited sequence (Y-n+1, Y-n+2,...) of futu re observations of the dependent variable. The intervals considered ha ve the interpretation that if the initial training sample belongs to a specified set G of ''good'' outcomes, the conditional coverage probab ility for each future confidence interval will be at least the nominal value. The set G is constructed to occur with high probability. All m ethods for constructing calibration intervals currently in the literat ure are conservative in that they are obtained from simultaneous toler ance intervals for which the actual confidence lever exceeds the nomin al level. This work develops constant-width simultaneous tolerance int ervals for which the bound on the nominal coverage probabilities is ex act under normality. The resulting confidence intervals represent an a ttractive balance between efficiency and simplicity for linear calibra tion problems.