  Consider a logistic partially linear model, in which the logit of the mean of
a binary response is related to a linear function of some covariates and a
nonparametric function of other covariates. We derive simple, doubly robust
estimators of coefficient for the covariates in the linear component of the
partially linear model. Such estimators remain consistent if either a nuisance
model is correctly specified for the nonparametric component, or another
nuisance model is correctly specified for the means of the covariates of
interest given other covariates and the response at a fixed value. In previous
works, conditional density models are needed for the latter purposes unless a
scalar, binary covariate is handled. We also propose two specific doubly robust
estimators: one is locally-efficient like in our class of doubly robust
estimators and the other is numerically and statistically simpler and can
achieve reasonable efficiency especially when the true coefficients are close
to 0.
