Smooth nonparametric estimation under monotonicity constraints

In this thesis we address the problem of estimating a curve of interest (which might be a probability density, a failure rate or a regression function) under monotonicity constraints. The main concern is investigating large sample distributional properties of smooth isotonic estimators, which have a faster rate of convergence and a nicer...

Central limit theorems for the Lp-error of smooth isotonic estimators

We investigate the asymptotic behavior of the Lp-distance between<br/>a monotone function on a compact interval and a smooth estimator<br/>of this function. Our main result is a central limit theorem for the Lp-error<br/>of smooth isotonic estimators obtained by smoothing a Grenander-type<br/>estimator or isotonizing the ordinary kernel...