  For regression models, most of existing specification tests can be
categorized into the class of local smoothing tests and of global smoothing
tests. Compared with global smoothing tests, local smoothing tests can only
detect local alternatives distinct from the null hypothesis at a much slower
rate when the dimension of predictor vector is high, but can be more sensitive
to oscillating alternatives. In this paper, we suggest a projection-based test
to bridge between the local and global smoothing-based methodologies such that
the test can benefit from the advantages of these two types of tests. The test
construction is based on a kernel estimation-based method and the resulting
test becomes a distance-based test with a closed form. The asymptotic
properties are investigated. Simulations and a real data analysis are conducted
to evaluate the performance of the test in finite sample cases.
