On a Small Sample Adjustment for the Profile Score Function in Semiparametric Smoothing Models

We consider the profile score function in models with smooth and
parametric components. If local respectively weighted likelihood
estimation is used for fitting the smooth component, the resulting
profile likelihood estimate for the parametric component is
asymptotically efficient as shown in Severini&Wong (Annals of
Statist., 1992). However, as in solely parametric models the
profile score function is not unbiased. We propose a small sample
bias adjustment which results by extending the correction suggested
in McCullagh&Tibshirani (JRSS B, 1990) to the framework of
semiparametric models.