(Received June 8, 1992; revised August 2, 1993)
Abstract. 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.
Key words and phrases: Asymptotic distribution, local alternatives, nonparametric regression, Monte Carlo.
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