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¹Ûµã×ÛÊö£ºIn this talk, we present a novel model checking method for functional linear quantile regression model (FLQRM). FLQRMis widely used to characterize the relationship between a scalar response and a functional covariate. Most existing research results are based on a correct assumption that the response is related to the functional predictor through a linear model for given quantile level. Thistalkfocuses on investigating the adequacy check of the functional linear quantile regression model. We propose a nonparametric kernel-based test statistic by using the functional principal component analysis. It is proved that the test statistic follows a normal distribution asymptotically under the null hypothesis and diverges to infinity for any misspecified models. Therefore, the test is consistent against any fixed alternative. Moreover, it is shown that the test has asymptotic power one for the local alternative hypothetical models converging to the null hypothesis. The finite sample properties of the test statistic are illustrated through extensive simulation studies. A real data set of 24 hourly measurements of ozone levels in Sacramento, California is analyzed by the proposed test.
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