For regressions with high-dimensional predictors, how to deal with data sparseness problem is an important issue. Existing local smoothing and global smoothing tests respectively shape into two very different classes of tests in this area, which have their own pros and cons in high-dimensional scenarios. In this project, we propose two novel approaches to bridge these two different methodologies. The first is to transfer a projection-based local smoothing test to be a global smoothing test such that the constructed test can benefit the advantages of two methods. The second is to use a model-adaptation method and a hybrid strategy to construct test statistic. Under the null hypothesis, the test is simply a sum of weighted residuals such that the critical values can be easily determined by normal distribution. While, under the alternative hypothesis the test automatically adapts to the underlying models so that general alternative hypothesis can be detected as any omnibus test does. The constructed tests by these two approaches can detect the alternatives distinct from the null at parametric rate that is fastest possible rate in hypothesis testing no matter the tests are constructed basing on local smoothing tests or not.
|Effective start/end date||1/01/19 → 31/12/22|
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