Inference and Estimation in a Changepoint Regression Problem

The two-line model when the location of the changepoint is known is introduced, with an F-test to detect a change in the regression coefficient. The situation when the changepoint is unknown is then introduced and an algorithm proposed for parameter estimation. It is demonstrated that when the location of the changepoint is not known the F-test does not conform to its expected parametric distribution. Nonparametric bootstrap methods are proposed as a way of overcoming the problems encountered. Finally, a physiology example is introduced where the regression change represents the change from aerobic to anaerobic energy production.