  A profile likelihood ratio test is proposed for inferences on the index
coefficients in generalized single-index models. Key features include its
simplicity in implementation, invariance against parametrization, and
exhibiting substantially less bias than standard Wald-tests in finite-sample
settings. Moreover, the R routine to carry out the profile likelihood ratio
test is demonstrated to be over two orders of magnitude faster than the
recently proposed generalized likelihood ratio test based on kernel regression.
The advantages of the method are demonstrated on various simulations and a data
analysis example.
