Data-Driven Smoothing Parameter Selection for Estimating Average Treatment Effects

• Activity Number: 410
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jenny Häggström*+ and Xavier de Luna
• Companies: Umeå University and Umeå University
• Keywords: Causal inference ; Double smoothing ; Local linear regression ; Smoothing parameter

Abstract

The nonparametric estimation of average treatment effects in observational studies 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 interest lies in estimating an average treatment effect. For that 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 can yield lower empirical mean squared error than other methods available such as, e.g., cross-validation.