L_2 Differentiability of Generalized Linear Models

TL;DR

This paper establishes conditions for the $L_2$ differentiability of generalized linear models, including those with non-exponential family error distributions, applicable to both stochastic and deterministic regressors, impacting GLM-based time series analysis.

Contribution

It provides new conditions for $L_2$ differentiability in GLMs with broader error distributions, extending existing theory to more general settings.

Findings

Derived $L_2$ differentiability conditions for generalized linear models.

Extended differentiability analysis to models with non-exponential family errors.

Applied conditions to GLM-based time series models.

Abstract

We derive conditions for $L_2$ differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions induce smoothness and integrability conditions for corresponding GLM-based time series models.