Change-Point Detection With Non-Parametric Regression

Lajos Orváth · Piotr S. Kokoszka

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Advanced Statistical Process Monitoring Statistical Methods and Inference Advanced Statistical Methods and Models

Abstract

We consider the regression model yi = ƒ(xi ) + ε in which the function ƒ or its pth derivative ƒ(p) may have a discontinuity at some unknown point τ. By fitting local polynomials from the left and right, we test the null that ƒ(p) is continuous against the alternative that ƒ(p)(τ−) ≠ ƒ(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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References

1997Limit theorems in change-point analysis 1993Nonparametric Methods in Change-Point Problems 1996Change point estimation using nonparametric regression 1993Tests for Change-Points with Epidemic Alternatives

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2009Change‐Point Tests for the Error Distribution in Non‐parametric Regression 2004Detection of a change point with local polynomial fits for the random design case 2010On rapid change points under long memory 2007Change-Point Estimation in Long Memory Nonparametric Models with Applications 2012Ratio tests for variance change in nonparametric regression

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