  The non-parametric estimation of average causal effects in observational
studies often relies on controlling for confounding covariates through
smoothing regression methods such as kernel, splines or local polynomial
regression. Such regression methods are tuned via smoothing parameters which
regulates the amount of degrees of freedom used in the fit. In this paper we
propose data-driven methods for selecting smoothing parameters when the
targeted parameter is an average causal effect. For this purpose, we propose to
estimate the exact expression of the mean squared error of the estimators.
Asymptotic approximations indicate that the smoothing parameters minimizing
this mean squared error converges to zero faster than the optimal smoothing
parameter for the estimation of the regression functions. In a simulation study
we show that the proposed data-driven methods for selecting the smoothing
parameters yield lower empirical mean squared error than other methods
available such as, e.g., cross-validation.
