A uniform Berry--Esseen theorem on $M$-estimators for geometrically ergodic Markov chains

Loïc Hervé, James Ledoux, Valentin Patilea

Let $\{X_n{\}}_{n\ge 0}$ be a $V$-geometrically ergodic Markov chain. Given some real-valued functional $F$, define $M_n(\alpha ):=n^{-1}{\sum }_{k=1}^{n}F(\alpha ,X_{k-1},X_k)$, $α\in\mathcal{A}\subs…