Abstract:
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This paper considers testing the predictive significance of the predictor using nonparametric regression. If a predictor has no predictive significance, the nonparametric regression function of the predictor will be constant and has zero variance. We propose a new hypothesis test of zero variance of the regression function. We present the technical proofs for the asymptotic theory of the test statistics and a method for estimating the percentiles of the limiting distribution. Using p-values from this test, and multiple testing ideas, a feature screening method in an ultrahigh dimensional setting is proposed, which can select groups of variables by the marginal predictive significance. The result of simulation studies shows the competitive performance of the test compares to other procedures. The proposed feature screening procedure is applied to a real data set in a genome-wide association study.
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