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We prove a semiparametric Bernstein-von Mises theorem for a homoskedasticpartially linear regression model with independent priors for thelow-dimensional parameter of interest and the infinite-dimensional nuisanceparameters. Our result avoids a prior invariance condition that arises from aloss of information in not knowing the nuisance parameter. The key idea is afeasible reparametrization of the regression function that mimics the Gaussianprofile likelihood. Such a device allows a researcher to assume independentpriors for the model parameters while automatically accounting for loss ofinformation associated with not knowing the nuisance parameter. As these priorstability conditions often impose strong restrictions on the underlyingdata-generating process, our results provide a more robust asymptotic normalitytheorem than the original parametrization of the partially linear model.

Parametrization, Prior Independence, and the Semiparametric Bernstein-von Mises Theorem for the Partially Linear Model