A note on unconditional properties of a parametrically guided Nadaraya-Watson estimator

Asymptotic properties of a semiparametric regression estimator proposed in Glad (1996) are derived, without conditioning on the predictor variables. The leading terms of unconditional asymptotic bias and variance are equal to those in the expressions obtained conditioned on the design in Glad (1996), while the unconditional approximations derived in this paper are of higher accuracy.