Simultaneous confidence intervals in inverse linear regression

Abstract

SUMMARY Suppose that we are concerned with estimates of the parameters in a linear regression model and with a large number of observations of the dependent variable. Different observations may correspond to different values of the independent variable. The problem of finding simultaneous confidence intervals for the values of the independent variable is considered. Asymptotically the probability of the event, that at least a prescribed proportion p of the intervals contains the true parameter, should exceed a prescribed number 1—δ.