The limit distribution of the L? -error of Grenander-type estimators

Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant

We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L k -type distances. In the case of a uniform distribution, we also establish...

The behavior of the NPMLE of a decreasing density near the boundaries of the support

Asymptotic normality of the Lk-error of the Grenander estimator

We investigate the limit behavior of the Lk-distance between a decreasing density f and its nonparametric maximum likelihood estimator ˆ fn for k ? 1. Due to the inconsistency of ˆ fn at zero, the case k = 2.5 turns out to be a kind of transition point.We extend asymptotic normality of the L1-distance to the Lk-distance for 1 ? k < 2.5, and...