Detection of a change point with local polynomial fits for the random design case

Summary Regression functions may have a change or discontinuity point in the ν th derivative function at an unknown location. This paper considers a method of estimating the location and the jump size of the change point based on the local polynomial fits with one-sided kernels when the design points are random. It shows that the estimator of the location of the change point achieves the rate n −1/(2ν+1) when ν is even. On the other hand, when ν is odd, it converges faster than the rate n −1/(2ν+1) due to a property of one-sided kernels. Computer simulation demonstrates the improved performance of the method over the existing ones.

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