Non‐parametric heteroscedastic transformation regression models for skewed data with an application to health care costs

Summary. We develop a new non‐parametric heteroscedastic transformation regression model for predicting the expected value of the outcome of a patient with given patient's covariates when the distribution of the outcome is highly skewed with a heteroscedastic variance. In our model, we allow both the transformation function and the error distribution function to be unknown. We show that under some regularity conditions the estimators for regression parameters, the expected value of the original outcome and the transformation function converge to their true values at the rate n−1/2. In our simulation studies, we demonstrate that our proposed non‐parametric method is robust with little loss of efficiency. Finally, we apply our model to a study on health care costs.