  We consider a one dimensional sub-ballistic random walk evolving in a
parametric i.i.d. random environment. We study the asymptotic properties of the
maximum likelihood estimator (MLE) of the parameter based on a single
observation of the path till the time it reaches a distant site. In that
purpose, we adapt the method developed in the ballistic case by Comets et al
(2014) and Falconnet, Loukianova and Matias (2014). Using a supplementary
assumption due to the specificity of the sub-ballistic regime, we prove
consistency and asymptotic normality as the distant site tends to infinity. To
emphazis the role of the additional assumption, we investigate the Temkin model
with unknown support, and it turns out that the MLE is consistent but, unlike
in the ballistic regime, the Fisher information is infinite. We also explore
the numerical performance of our estimation procedure.
