For journals title abbreviations, Estat. or estat. is used, for instance, by the Revista Brasileira de Estatística, which is abbreviated to R. Bras. Estat. This is also the rule for abbreviation of titles to periodicals and other serials set by the Brazilian Association of Technical Standards (ABNT), NBR 6032.
As Valdeir Psr points out in his comment, the Academia Brasileira de Letras provides a list of common abbreviations, which includes:
Of these, the first indeed seems more common (and useful) to me.
In physics, Mecânica Estatística is sometimes colloquially referred to as "mecstat", especially by students. Though I haven't seen any other context where "stat" is an accepted abbreviation of "estatística", using the English "Stats" in an interface might be an acceptable, if inelegant solution.