Change-Point Detection With Non-Parametric Regression |
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Authors: | Lajos Orváth Piotr Kokoszka |
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Institution: | 1. Department of Mathematics , University of Utah , Salt Lake City, UT, 84112, USA E-mail: horvath@math.utah.edu;2. Department of Mathematical Sciences , University of Liverpool , Liverpool, L69 3BX, UK E-mail: P.S.Kokoszka@liverpool.ac.uk |
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Abstract: | We consider the regression model yi = ?(xi ) + ε in which the function ? or its pth derivative ?(p) may have a discontinuity at some unknown point τ. By fitting local polynomials from the left and right, we test the null that ?(p) is continuous against the alternative that ?(p)(τ?) ≠ ?(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. |
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Keywords: | Nonparametric Change-point Tests Polynomial Smoothing |
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