Seminar| Institute of Mathematical Sciences
Abstract: There are lots of variable selection proposals for longitudinal data, but virtually no solutions following the model-free strategy. As such, we propose a novel variable selection method in sufficient dimension folding, based on a newly introduced sufficient dimension reduction (SDR) method. It is model-free without estimating link function or relying on slicing technique. And it can screen out irrelevant and redundant variables while naturally keeping the correlation structure in longitudinal data. Moreover, the proposed SDR method can also be used to construct an adaptiveto-model test for checking the marginal parametric single-index models. The test not only can inherit the merits of the local smoothing tests that have tractable limiting null distributions and are sensitive to oscillating alternative models, but also can greatly alleviate the curse of dimensionality in the sense that it behaves like a test with only one covariate. This results in better significance level maintenance and higher power than the classical tests. The finite sample performance of the variable selection and model checking procedures is demonstrated through Monte Carlo studies and analysis of a primary biliary cirrhosis data set.