|
Abstract:
|
We propose a regularized efficient score estimation and testing (RESET) approach for treatment effects in the presence of nuisance parameters, in low-dimensional and high-dimensional generalized linear models. The RESET approach is based on estimating the efficient score function of the treatment parameters. This means we are trying to remove the influence of nuisance coefficients on the treatment parameter and construct an efficient score function which could be used for estimating and testing for the treatment parameter. As the simulation results show, our RESET approach is comparable with the common used maximum likelihood estimators with a smaller standard error in most cases. We also proved that the RESET one-step estimator is consistent to the true parameter under some regularized conditions, either in low-dimensional or high-dimensional models. Also, the efficient score function of the treatment parameter follows a chi-square distribution, which will be used for hypothesis testing for the treatment effect. In order to evaluate the finite sample performance of the RESET approach, simulation studies are conducted, followed by a real data example to demonstrate its application.
|
