Exact two-sided confidence sets for a level set in simple linear regression

Abstract

Regression modeling is the workhorse of statistics. It is realized in recent years that one important aim in regression analysis may be the estimation of a level set of the regression function. The published work on this has thus far focused mainly on nonparametric regression, especially on point estimation. In our previous work, we constructed exact upper and lower, but only conservative two-sided, confidence sets for a level set in linear regression. In this paper, exact two-sided confidence sets are constructed in simple linear regression. A simultaneity property of the exact two-sided confidence is also studied. An example is given to illustrate the method.