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Title: Adaptive model checking for functional single-index models Authors:  Qing Jiang - Beijing Normal University (China) [presenting]
Feifei Chen - Renmin University of China (China)
Zhenghui Feng - School of Economics \& Wang Yanan Institute for studies in Economics, Xiamen University (China)
Abstract: Functional model checking is seldom studied in the literature because of the infinite dimension trouble. A model-adaptive test statistic is proposed to do model checking for functional single-index models. Dimension reduction methods are included to handle the curse of dimensionality. The test consists of two parts: the first term is a naive one, and the second term is adaptive to the model as if the model were univariate, and with higher power. It is consistent against any global alternative hypothesis and can detect local alternative at a fast rate. Simulation studies show the performance compared with other methods.