Boosting on the responses with Tweedie loss functions

Hainaut et al. (2022) showed that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each iteration step. In this short note, we complete the results obtained in Hainaut et al. (2022) by showing that among the usual link functions, the log-link function is actually the only one for which boosting can be regarded as an iteratively re-weighted procedure applied to the original data.