Trends in Moderate Rainfall Extremes: A Regional Monotone Regression Approach

Rainfall extremes are thought to have increased over recent years. Typically linear trends have been considered to describe the temporal evolution of high quantiles of the daily rainfall distribution. For long records it is important to allow more flexibility. Quantile regression methods are available to estimate monotone trends for single...

Nonparametric confidence intervals for monotone functions

We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699–1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions,...

Projections of precipitation extremes based on a regional, non-stationary peaks-over-threshold approach: A case study for the Netherlands and north-western Germany

Projections of extreme precipitation are of great importance, considering the potential severe impacts on society. In this study a recently developed regional, non-stationary peaks-over-threshold approach is applied to two transient simulations of the RACMO2 regional climate model for the period 1950–2100, driven by two different general...

A regional peaks-over-threshold model in a nonstationary climate

Regional frequency analysis is often used to reduce the uncertainty in the estimation of distribution parameters and quantiles. In this paper a regional peaks-over-threshold model is introduced that can be used to analyze precipitation extremes in a changing climate. We use a temporally varying threshold, which is determined by quantile...

Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function in this model is the nonparametric maximum likelihood estimator (MLE). We study two alternative methods for...

Estimating a concave distribution function from data corrupted with additive noise

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0, ?). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational...

Statistiek in vorm

Asymptotics: Particles, Processes and Inverse Problems. Festschrift for Piet Groeneboom

Estimation of a convex function: Characterizations and asymptotic theory

We study nonparametric estimation of convexregression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case).We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of...

A canonical process for estimation of convex functions: The "invelope" of integrated Brownian motion +t4

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian...

Integrated Brownian Motion, Conditioned to be Positive

We study the two-dimensional process of integrated Brownian motion and Brownian motion, where integrated Brownian motion is conditioned to be positive. The transition density of this process is derived from the asymptotic behavior of hitting times of the unconditioned process. Explicit expressions for the transition density in terms of confluent...

Isotonic inverse estimators for nonparametric deconvolution

A new nonparametric estimation procedure is introduced for the distribution function in a class of deconvolution problems, where the convolution density has one discontinuity. The estimator is shown to be consistent and its cube root asymptotic distribution theory is established. Known results on the minimax risk for the estimation problem...

Three Statistical Inverse Problems: Estimators-algorithms-asymptotics

Isotonic estimation and rates of convergence in Wicksell's problem