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Test for the parametric part in partial functional linear regression based on B-spline

Abstract In this paper, we investigate the hypothesis test of the parametric component in partial functional linear regression model based on B-spline. The test statistic is constructed by using the residual sums of squares under the null and alternative hypothesis. We show that the limiting distribution of the test statistic under the null hypothesis is the chi-square distribution. Besides, as the sample size goes to infinity, we prove that the power of the proposed test approaches 1. The finite sample performance of our test is evaluated by a simulation study. Also, we compare our method with existing method.