Assumption-Lean Regression for Nonnegative Response via Variational Representation

We present a novel estimator for regression parameters that does not require any assumptions about the conditional distribution family of the response variable, except for non-negativity. This estimator is particularly useful for handling semi-continuous, zero-inflated, and proportional data, eliminating the need for complex models and simplifying the inference process. The estimator is unaffected by over-under dispersion, heavy tails or other problems related to the incorrect assumptions about the response distribution. In addition, the asymptotic properties of the estimator do not depend on the underlying conditional distribution. Apart from that, our method does not involve kernel-based estimation and is, therefore, free from issues related to smoothing parameter selection. The R code for implementing the method and reproducing the results is available in the supplementary materials.