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Title: Model checking for the single-index model: A residual decomposition approach Authors:  Yih-Huei Huang - Tamkang University (Taiwan) [presenting]
Abstract: The single-index model is a popular semiparametric model. It has the flexibility of nonparametric regression and avoids the curse of dimensionality by adopting a single-index, instead of the whole covariate, as the predictor in the regression model. It has been widely used and a few diagnostic tools or goodness of fit tests had been developed for model checking. Nevertheless, there are drawbacks for traditional approaches. Existent tests could be complicated to implement, require quite an amount of computation or not powerful for certain alternative hypothesis. Motivated by these drawbacks. We decomposed the residual and found the conditions when the test statistics is asymptotic distribution free. It is easy in implementation, require no bootstrapping and has good power performance according to a small simulation study.