  I prove a semiparametric Bernstein-von Mises theorem for a partially linear
regression model with independent priors for the low-dimensional parameter of
interest and the infinite-dimensional nuisance parameters. My result avoids a
prior invariance condition that arises from a loss of information in not
knowing the nuisance parameter. The key idea is a feasible reparametrization of
the regression function that mimics the Gaussian profile likelihood. This
allows a researcher to assume independent priors for the model parameters while
automatically accounting for the loss of information associated with not
knowing the nuisance parameter. As these prior stability conditions often
impose strong restrictions on the underlying data-generating process, my
results provide a more robust asymptotic normality theorem than the original
parametrization of the partially linear model.
