  In what follows we study non asymptotic behavior of different well known
estimators AIC(\cite{Tong}), BIC(\cite{Schwarz}) and EDC(\cite{Zhao,Dorea}) in
contrast with the Markov chain order estimator, named as Global Depency Level -
GDL(\cite{Baigorri}).
  The estimator GDL, is based on a different principle which makes it behave in
a quite different form. It is strongly consistent and more efficient than
AIC(inconsistent), outperforming the well established and consistent BIC and
EDC, mainly on relatively small samples.
  The estimators mentioned above mainly consist in the evaluation of the Markov
chain's sample by different multivariate deterministic functions. The log
likelihood approach or the GDL approach, shall be analysed exhibiting different
structural properties. It will become clear the intimate differences existing
between the variance of both estimators, which induce quite dissimilar
performance, mainly for samples of moderated sizes.
