Change-Point Detection With Non-Parametric Regression

Lajos Orváth, Piotr Kokoszka
2002 Statistics (Berlin)  
We consider the regression model y i ¼ f ðx i Þ þ e in which the function f or its pth derivative f ðpÞ may have a discontinuity at some unknown point t. By fitting local polynomials from the left and right, we test the null that f ðpÞ is continuous against the alternative that f ðpÞ ðtÀÞ 6 ¼ f ðpÞ ðtþÞ. We obtain Darling-Erd} o os 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
more » ... Consistency of the related change-point estimators is also established.
doi:10.1080/02331880210930 fatcat:j25fxhalr5du3nedzgv57dwaaq