Testing for a monotone density using $L_k$-distances between the empirical distribution function and its concave majorant
Vladimir N. Kulikov and Hendrik P. Lopuhaa
(2004) Technical Report. EURANDOM, the Netherlands.

## Abstract

We prove asymptotic normality for $L_k$-functionals $\int |\hat F_n-F_n|^k g(t)\,dt$, where $F_n$ is the empirical distribution function of a sample from a decreasing density and $\hat F_n$ is the least concave majorant of $F_n$. From this we derive two test statistics for the null hypothesis that a probability density is monotone. These tests are compared with existing proposals such as the supremum distance between $\hat F_n$ and $F_n$.

EPrint Type: Monograph (Technical Report) Project Keyword UNSPECIFIED Learning/Statistics & Optimisation 792 Vladimir Koulikov 30 December 2004