Testing for changes in polynomial regression. (English) Zbl 1155.62027

Aue, Alexander; Horváth, Lajos; Hušková, Marie; Kokoszka, Piotr

Bernoulli 14, No. 3, 637-660 (2008).

Summary: We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability of the regression parameters against the alternative of a break at an unknown time. We derive the extreme value distribution of a maximum-type test statistic which is asymptotically equivalent to the maximally selected likelihood ratio. The resulting test is easy to apply and has good size and power, even in small samples.

MSC:

62G08	Nonparametric regression and quantile regression
62G10	Nonparametric hypothesis testing
62G20	Asymptotic properties of nonparametric inference
62G32	Statistics of extreme values; tail inference
62E20	Asymptotic distribution theory in statistics

Keywords:

change-point analysis; extreme value asymptotics; Gaussian processes; Legendre polynomials; linear regression; polynomial regression

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