  This paper deals with a nonparametric shape respecting estimation method for
U-shaped or unimodal functions. A general upper bound for the nonasymptotic
L_1-risk of the estimator is given. The method is applied to the shape
respecting estimation of several classical functions, among them typical
intensity functions encountered in the reliability field. In each case, we
derive from our upper bound the spatially adaptive property of our estimator
with respect to the L_1-metric: it approximately behaves as the best variable
binwidth histogram of the function under estimation.
