Bounded Length Confidence Intervals for the Zero of a Regression Function

The problem of determining a bounded length confidence interval for the zero of a regression function R () is discussed. In case R () = F () - p, F a distribution function, 0 p 1, a closed stopping rule is given for the up-down method of experimentation. For a larger class of regression functions a closed stopping rule is given for Robbins-Monro type of experimentation. The stopping rule for the Robbins-Monro process depends on prior knowledge of an upper and a lower bound on the zero of R (). It is shown that given suitable assumptions about the random variables used in experimentation finite confidence intervals for the zero of R () may be found, such confidence intervals providing an upper and a lower bound on the zero of R () with prespecified level of confidence.