|
Abstract:
|
Although most real data consist of a mix of discrete and continuous predictors, many existing sufficient dimension reduction methods are designed for data with elliptical predictor distribution, which excludes discrete predictors. Some methods avoid this restriction by utilizing local kernel regression, although these methods also struggle with discrete predictors. To fill this critical gap, we propose projection expectile regression (PER) as a new sufficient dimension reduction method that overcomes this problem. Our proposal does not involve kernel smoothing or matrix inversion. Therefore, PER is applicable in a wide variety of applications. We demonstrate the superior performance of projection expectile regression in synthetic data and real data analyses of health insurance charges. We also provide the asymptotic properties of the PER estimator.
|
