A1000
Title: Estimation of functional treatment effect using generalized empirical likelihood stabilized weights
Authors: Ruoxu Tan - The University of Hong Kong (Hong Kong) [presenting]
Wei Huang - University of Melbourne (Australia)
Guosheng Yin - The University of Hong Kong (Hong Kong)
Zheng Zhang - Renmin University of China (China)
Abstract: Most studies concerning the effect of a functional variable on an outcome are restricted to exploring the association rather than the casual relationship. In the areas where causal treatment effect analysis has many applications, functional data has become popular in the recent decade. Due to the lack of definition of probability density function for functional data, estimating the propensity score for functional treatment is challenging. The limited literature on the functional treatment effect tackled this problem by replacing the functional treatment with its functional principal component scores in the definition of the propensity score. However, such an approximation does not guarantee asymptotic consistency. We propose not using the principal component scores but identifying the average treatment effect by a weighted conditional expectation of the observed outcome given the functional treatment. The weights, called the stabilized weights, can be well defined in terms of a functional treatment. We then estimate the stabilized weights using a generalized empirical likelihood method and show the consistency of our estimator. After that, a functional linear estimator of the average treatment effect is proposed. We study the theoretical and numerical properties of the estimator. A real data application demonstrates the practical value of our method.
