Cécile Durot

A Kolmogorov-type test for monotonicity of regression

A new nonparametric procedure for testing monotonicity of a regression mean is proposed. The test is shown to have prescribed asymptotic level and good asymptotic power. It is based on the supremum distance from an empirical process to its least concave majorant and is very easily implementable. A simulation study is reported to demonstrate finite sample behavior of the procedure.

On the -error of monotonicity constrained estimators

We aim at estimating a function

On the distance between the empirical process and its concave majorant in a monotone regression framework

\lambda:[0,1]\to \mathbb {R}

Least-squares estimation of a convex discrete distribution

, subject to the constraint that it is decreasing (or increasing). We provide a unified approach for studying the

Monotone Nonparametric Regression with Random Design

\mathbb {L}_p

A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation

-loss of an estimator defined as the slope of a concave (or convex) approximation of an estimator of a primitive of

Testing Convexity or Concavity of a Cumulated Hazard Rate

\lambda

Testing monotonicity via local least concave majorants

, based on

On asymptotics of the discrete convex LSE of a p.m.f.

n

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

observations. Our main task is to prove that the