TESTING FOR NO EFFECT IN NONPARAMETRIC REGRESSION VIA SPLINE SMOOTHING TECHNIQUES

JUEI-CHAO CHEN

Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung 40724, Taiwan, ROC

(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.