Joint sufficient dimension reduction for estimating continuous treatment effect functions.

Area of Science:

• Statistics
• Econometrics
• Causal Inference

Background:

• Estimating continuous treatment effects from observational data often relies on restrictive parametric models.
• Nonparametric methods face the curse of dimensionality with high-dimensional covariates.
• Dimension reduction is crucial for balancing model flexibility and parsimony.

Purpose of the Study:

• To propose a sufficient dimension reduction framework for estimating continuous treatment effect functions.
• To overcome the limitations of existing parametric and nonparametric approaches.
• To enable accurate estimation without pre-specifying the dimension of the central subspace.

Main Methods:

• Utilizing a sufficient dimension reduction framework to identify a lower-dimensional subspace.
• Estimating the joint central subspace at an *n*^1/2-rate.
• Employing local estimation within the reduced dimension and a non-standard infinitesimal jackknife for joint parameter estimation.

Main Results:

• The proposed method effectively reduces dimensionality while maintaining flexibility.
• The joint central subspace is estimated at a fast *n*^1/2-rate.
• Efficient joint estimation of multiple smoothing parameters for continuous treatments is achieved.

Conclusions:

• The sufficient dimension reduction framework offers a powerful approach for continuous treatment effect estimation.
• This method provides a more flexible and computationally feasible alternative to existing techniques.
• The study advances the methodology for causal inference with continuous treatments in observational studies.