  In this paper, we are interested in the study of beta kernel estimators from
an asymptotic minimax point of view. It is well known that beta kernel
estimators are, on the contrary of classical kernel estimators, "free of
boundary effect" and thus are very useful in practice. The goal of this paper
is to prove that there is a price to pay: for very regular functions or for
certain losses, these estimators are not minimax. Nevertheless they are minimax
for classical regularities such as regularity of order two or less than two,
supposed commonly in the practice and for some classical losses.
