Title: Multiple use confidence intervals for the statistical calibration problem
Authors: Martina Chvostekova - Institute of Measurement Science of Slovak Academy of Sciences (Slovakia) [presenting]
Abstract: The statistical calibration problem consists of constructing the interval estimates for future unobserved values of an explanatory variable, say $x$, corresponding to possibly infinitely many future observations of a response variable, say $y$, based on $n$ pairs of values $(x_i,y_i)$, $i = 1, 2, \ldots, n$. In the basic setting of the model it is assumed a linear dependence between the variables, a polynomial regression is probably the most frequently used model in industrial applications, and the measurements errors of the observation variable are independent normally distributed variables with zero mean and a common unknown variance. A marginal property of the multiple use confidence intervals is that at least $\gamma$ proportion of them contains the corresponding true value of the explanatory variable with confidence $1 - \alpha$. One standard way to construct the multiple use confidence intervals is to invert $(\gamma, 1 - \alpha)$ simultaneous tolerance intervals for a linear regression, but such multiple use confidence intervals are conservative. It is proposed a procedure for determining the exact multiple use confidence intervals under assuming a distribution of the explanatory variable. The computation of the suggested multiple use confidence intervals is fast and they are uniformly narrower than previously published.