Gebundelde krachten

Statistic

Three Statistical Inverse Problems: Estimators-algorithms-asymptotics

Electrical Engineering, Mathematics and Computer Scienc

Statistiek in vorm

Electrical Engineering, Mathematics and Computer Scienc

A Conversation with Piet Groeneboom

Petrus (Piet) Groeneboom was born in Scheveningen in 1941 and grew up in Voorburg. Both villages are located near The Hague in The Netherlands; Scheveningen actually being part of The Hague. He attended the gymnasium of the Huygens lyceum. In 1959, he entered the University of Amsterdam, where he studied psychology. After his “candidate” exam (comparable to BSc) in 1963, he worked at the psychological laboratory of the University of Amsterdam until 1966. In 1965, he took up mathematics as a part-time study. After having obtained his master’s degree in 1971, he had a position at the psychological laboratory again until 1973, when he was appointed to the Mathematical Center in Amsterdam. There, he wrote between 1975 and 1979 his Ph.D. thesis with Kobus Oosterhoff as advisor, graduating in 1979. After a period of two years as visiting professor at the University of Washington (UW) in Seattle, Piet moved back to the Mathematical Center until he was appointed full professor of statistics at the University of Amsterdam in 1984. Four years later, he moved to Delft University of Technology where he became professor of statistics and stayed until his retirement in 2006. Between 2000 and 2006 he also held a part-time professorship at the Vrije Universiteit in Amsterdam. From 1999 till 2013 he was Affiliate Professor at the statistics department of UW, Seattle. Apart from being visiting professor at the UW in Seattle, he was also visiting professor at Stanford University, Université Paris 6 and ETH Zürich. Piet is well known for his work on shape constrained statistical inference. He worked on asymptotic theory for these problems, created algorithms to compute nonparametric estimates in such models and applied these models to real data. He also worked on interacting particle systems, extreme value analysis and efficiency theory for testing procedures. Piet (co-)authored four books and 64 papers and served as promotor of 13 students. He is the recipient of the 1985 Rollo Davidson prize, a fellow of the IMS and elected member of the ISI. In 2015, he delivered the Wald lecture at the Joint Statistical Meeting in Montreal. Piet and his wife Marijke live in Naarden. He has two sons, Thomas and Tim, and (since June 12, 2018) one grandson, Tarik. This conversation was held at Piet’s house in Naarden, on February 28 and April 24, 2018.Statistic

Isotonic estimation and rates of convergence in Wicksell's problem

Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Some Developments in the Theory of Shape Constrained Inference

Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.Statistic

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 positive curvature of the functions estimated. The asymptotic distribution theory relies on the existence of an “invelope function” for integrated two-sided Brownian motion $+t^4$ which is established in a companion paper by Groeneboom, Jongbloed and Wellner.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

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 stations. Having multiple stations in a region, the significance of the trend at the regional scale is often of interest. From this perspective the authors propose a regression approach that can be used to estimate a common monotone trend for the site-specific quantiles. Moreover, the method allows for the construction of confidence bands and testing the hypothesis of an existing nondecreasing trend against the null hypothesis of no trend. The approach is applied to 102 series of daily rainfall over the Netherlands for the period 1910–2009. The results are compared with those from a (regional) Mann–Kendall test. Significantly increasing trends are found for the winter season and for the whole year. In the summer season trends are less consistent over the region and are only significant in the western part of the Netherlands. For the summer season, linearity of the trend seems less apparent than for winter and for the whole year. However, the deviation from linearity is not significant.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Monotone trends in the distribution of climate extremes

The generalized Pareto distribution (GPD) is often used in the statistical analysis of climate extremes. For a sample of independent and identically distributed observations, the parameters of the GPD can be estimated by the maximum likelihood (ML) method. In this paper, we drop the assumption of identically distributed random variables. We consider independent observations from GPD distributions having a common shape parameter but possibly an increasing trend in the scale parameter. Such a model, with increasing scale parameter, can be used to describe a trend in the observed extremes as time progresses. Estimating an increasing trend in a distribution parameter is common in the field of isotonic regression. We use ideas and tools from that area to compute ML estimates of the GPD parameters. In a simulation experiment, we show that the iterative convex minorant (ICM) algorithm is much faster than the projected gradient (PG) algorithm. We apply the approach to the daily maxima of the central England temperature (CET) data. A clear positive trend in the GPD scale parameter is found, leading to an increase in the 100-year return level from about 31º in the 1880s to 34º in 2015.Delft Institute of Applied Mathematic

Smooth estimation of size distributions in an oriented cylinder model

Kernel estimators are proposed for estimating the cumulative distribution functions and the probability density functions of several quantities of interest in a stereological oriented cylinder model. This oriented cylinder model was developed to represent anisotropic microstructural features in materials. The asymptotic properties of these estimators are studied, and the estimators are applied to two banded dual phase steel microstructures. The estimation method is quite general and can also be applied to distributions of other univariate quantities of interest.Delft Institute of Applied MathematicsMaterials Science and Engineering(OLD) MSE-