  We consider a random walk in i.i.d. random environment with distribution
$\nu$ on Z. The problem we are interested in is to provide an estimator of the
cumulative distribution function (c.d.f.) F of $\nu$ from the observation of
one trajectory of the random walk. For that purpose we first estimate the
moments of $\nu$, then combine these moment estimators to obtain a collection
of estimators (F M n) M $\ge$1 of F , our final estimator is chosen among this
collection by Lepskii's method. This estimator is therefore easily computable
in practice. We derive convergence rates for this estimator depending on the
H{\"o}lder regularity of F and on the divergence rate of the walk. Our rate is
optimal when the chain realizes a trade-off between a fast exploration of the
sites, allowing to get more informations and a larger number of visits of each
sites, allowing a better recovery of the environment itself.
