Finite sample and asymptotic behaviour of the longitudinal outcome-highly-adaptive LASSO

Music City Center 

Longitudinal causal inference methods for non-stochastic interventions are sometimes severely limited by data sparsity due to the natural high-dimensionality of the longitudinal problem. Ad hoc statistical model smoothing is typically recommended in order to make the identifiability and estimation problem tractable. While nuisance functions with reduced dimensionality may be sufficient to identify the parameter of interest, the robust learning of these smoothed functions, and inference for the parameter of interest, have not yet been well-addressed in the literature. In this work, we propose a longitudinal version of the outcome-highly-adaptive LASSO that performs model smoothing in the time-point-specific propensity scores. We investigate the regular asymptotic linearity of the estimator both theoretically and empirically, and present results of the estimation variance reduction due to the smoothing procedure.

causal inference

longitudinal

time-dependent

nonparametric

machine-learning