Change-Point Detection With Non-Parametric Regression

We consider the regression model yi = ƒ(xi ) + ε in which the function ƒ or its pth derivative ƒ(p) may have a discontinuity at some unknown point τ. By fitting local polynomials from the left and right, we test the null that ƒ(p) is continuous against the alternative that ƒ(p)(τ−) ≠ ƒ(p)(τ+). We obtain Darling-Erdös type limit theorems for the test statistics under the null hypothesis of no change, as well as their limits in probability under the alternative. Consistency of the related change-point estimators is also established.