Summary: Semiparametric additive models (SAMs) are very useful in multivariate nonparametric regression. In this paper, the authors study nonparametric testing problems for the nonparametric components of SAMs. Using the backfitting algorithm and the local polynomial smoothing technique, they extend to SAMs the generalized likelihood ratio tests of J. Fan
and J. Jiang
[J. Am. Stat. Assoc. 100, No. 471, 890–907 (2005; Zbl 1117.62328
)]. The authors show that the proposed tests possess the Wilks-type property and that they can detect alternatives nearing the null hypothesis with a rate arbitrarily close to root-n while error distributions are unspecified. They report simulations which demonstrate the Wilks phenomenon and the powers of their tests. They illustrate the performance of their approach by simulation and using the Boston housing data set.