Projection expectile regression for sufficient dimension reduction.

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• Existing sufficient dimension reduction methods often assume elliptical predictor distributions, limiting their use with real-world data.
• Complex predictor structures (continuous, discrete, mixed) and stratified response surfaces pose challenges for traditional methods.
• Issues like multicollinearity, high dimensionality, and sparsity in predictors require robust dimension reduction techniques.

Purpose of the Study:

• To introduce Projection Expectile Regression (PER) as a novel linear sufficient dimension reduction method.
• To develop a method capable of handling diverse predictor variable types and non-smooth link functions.
• To address limitations of existing methods concerning predictor complexity and computational challenges.

Main Methods:

• Projection Expectile Regression (PER) is proposed, a linear sufficient dimension reduction technique.
• PER accommodates continuous, discrete, and mixed predictor variables.
• The method requires a monotone link function, allowing for stratified response surfaces without matrix inversion or high-dimensional smoothing.

Main Results:

• Extensive simulations demonstrate the effectiveness of PER on synthetic data.
• A real-world data analysis of US health insurance charges showcases PER's practical applicability.
• Asymptotic properties of the PER estimator are theoretically established.

Conclusions:

• PER provides a flexible and robust solution for sufficient dimension reduction with complex predictors.
• The method effectively manages multicollinearity, high dimensionality, and sparsity.
• PER is suitable for diverse datasets and offers theoretical guarantees for its estimator.