Eliminating residual confounding in the stratified estimator via smoothing along with the propensity score

) pointed it out that the stratified estimator can be regarded as a special case of the inverse probability weighting estimator with piecewise constant propensity score and proposed a method eliminating residual confounding in the stratified estimator. In this paper, we provide an alternative interpretation of the stratified estimator as the outcome regression with a piecewise constant function over the propensity score. By considering kernel smoothing, an estimator free from residual confounding is proposed based on the stratified estimator, which preserves the robustness of the stratified estimator. We also propose a doubly robust estimator, which does not rely on the inverse probability weighting.