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For regression models, most of existing specification tests can becategorized into the class of local smoothing tests and of global smoothingtests. Compared with global smoothing tests, local smoothing tests can onlydetect local alternatives distinct from the null hypothesis at a much slowerrate when the dimension of predictor vector is high, but can be more sensitiveto oscillating alternatives. In this paper, we suggest a projection-based testto bridge between the local and global smoothing-based methodologies such thatthe test can benefit from the advantages of these two types of tests. The testconstruction is based on a kernel estimation-based method and the resultingtest becomes a distance-based test with a closed form. The asymptoticproperties are investigated. Simulations and a real data analysis are conductedto evaluate the performance of the test in finite sample cases.

Specification testing for regressions: an approach bridging between local smoothing and global smoothing methods