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Detection of a change point with local polynomial fits for the random design case
Author(s) -
Huh J.,
Park B.U.
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00340.x
Subject(s) - mathematics , estimator , polynomial , jump , point (geometry) , discontinuity (linguistics) , change detection , function (biology) , property (philosophy) , algorithm , statistics , mathematical analysis , geometry , computer science , artificial intelligence , quantum mechanics , evolutionary biology , biology , philosophy , epistemology , physics
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.