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Testing for no effect in nonparametric regression via spline smoothing techniques

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We propose three statistics for testing that a predictor variable has no effect on the response variable in regression analysis. The test statistics are integrals of squared derivatives of various orders of a periodic smoothing spline fit to the data. The large sample properties of the test statistics are investigated under the null hypothesis and sequences of local alternatives and a Monte Carlo study is conducted to assess finite sample power properties.

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Chen, J. Testing for no effect in nonparametric regression via spline smoothing techniques. Ann Inst Stat Math 46, 251–265 (1994).

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Key words and phrases

  • Asymptotic distribution
  • local alternatives
  • nonparametric regression
  • Monte Carlo