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Detection of a change point with local polynomial fits for the random design case
Authors:J Huh  BU Park
Institution:Dept of Statistics, Duksung Women's University, Seoul, Korea; Dept of Statistics, Seoul National University, Seoul, Korea
Abstract: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.
Keywords:discontinuity point  non-parametric regression  one-sided kernel  rate of convergence  two-sided Brownian motion  weak convergence
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