The distance between a naive cumulative estimator and its least concave majorant

Hendrik P. Lopuhaä, Eni Musta

We consider the process ${\hat{\Lambda }}_n-{\Lambda }_n$, where ${\Lambda }_n$ is a cadlag step estimator for the primitive $\Lambda$ of a nonincreasing function $\lambda$ on $[0,1]$, and ${\hat{\Lambda }}_n$ is the least c…