The limit distribution of the $L_\infty$-error of Grenander-type estimators

Details The limit distribution of the $L_\infty$-error of Grenander-type estimators The limit distribution of the $L_\infty$-error of Grenander-type estimators

2011-11-25

arxiv.org/abs/1111.5934v1

Mathematics

Statistics Theory

Scientific paper

Let $f$ be a non-increasing function defined on $[0,1]$. Under standard
regularity conditions, we derive the asymptotic distribution of the supremum
norm of the difference between $f$ and its Grenander-type estimator on
sub-intervals of $[0,1]$. The rate of convergence is found to be of order
$(n/\log n)^{-1/3}$ and the limiting distribution to be Gumbel.

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