Let $\{X_n\}_{n\ge0}$ be a $V$-geometrically ergodic Markov chain. Given some real-valued functional $F$, define $M_n(��):=n^{-1}\sum_{k=1}^nF(��,X_{k-1},X_k)$, $��\in\mathcal{A}\subset \mathbb {R}$. Consider an $M$ estimator $\hat��_n$, that is, a measurable function of the observations satisfying $M_n(\hat��_n)\leq \min_{��\in\mathcal{A}}M_n(��)+c_n$ with $\{c_n\}_{n\geq1}$ some sequence of real numbers going to zero. Under some standard regularity and moment assumptions, close to those of the i.i.d. case, the estimator $\hat��_n$ satisfies a Berry--Esseen theorem uniformly with respect to the underlying probability distribution of the Markov chain.

Published in at http://dx.doi.org/10.3150/10-BEJ347 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)