| Summary: | 碩士 === 淡江大學 === 數學學系碩士班 === 104 === Single-Index models relax restrictive part of usual assumptions on parametric models. They are becoming popular in these years and are used in a various field statistic of economic, financial sector, biostatistics, medical science fields. In this paper, we study goodness-of-fit testing for Single-Index models. The semi-parametric approach make the complexity in the assessing of validness of the model. So, we adopted Huang & Wen (2016) approach. If the model is correctly specified, then the residual of the fitted model is orthogonal to functions of covariates. On the other hand, if the model assumption is incorrect, the residual will not be orthogonal to covariates. With this geometric relation, Huang (2016) develops a goodness-of-fit test based on whether certain inner products have zero means. In our thesis, we assess the performs of such projection approach by various simulation study. This is a novel approach and its performance is still unclear. We conduct a few simulation studies to asses the performance of the approach, and investigate the impacts of the bandwidth h selection, β ,σ2 and sample size on the power of the test.
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