  We aim at estimating a function $\lambda:[0,1]\to \mathbb {R}$, subject to
the constraint that it is decreasing (or increasing). We provide a unified
approach for studying the $\mathbb {L}_p$-loss of an estimator defined as the
slope of a concave (or convex) approximation of an estimator of a primitive of
$\lambda$, based on $n$ observations. Our main task is to prove that the
$\mathbb {L}_p$-loss is asymptotically Gaussian with explicit (though unknown)
asymptotic mean and variance. We also prove that the local $\mathbb {L}_p$-risk
at a fixed point and the global $\mathbb {L}_p$-risk are of order $n^{-p/3}$.
Applying the results to the density and regression models, we recover and
generalize known results about Grenander and Brunk estimators. Also, we obtain
new results for the Huang--Wellner estimator of a monotone failure rate in the
random censorship model, and for an estimator of the monotone intensity
function of an inhomogeneous Poisson process.
