How to determine the error of a Markov Chain Monte Carlo Output

This thesis discusses and compares methods which try to approximate the assymptotic variance.

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...

A central limit theorem for the Hellinger loss of Grenander-type estimators

We consider Grenander-type estimators for a monotone function (Formula presented.), obtained as the slope of a concave (convex) estimate of the primitive of λ. Our main result is a central limit theorem for the Hellinger loss, which applies to estimation of a probability density, a regression function or a failure rate. In the case of density...

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...