Searched for: author%3A%22Groeneboom%2C+P.%22
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Groeneboom, P. (author)
We analyze nonparametric estimators for the distribution function of the incubation time in the singly and doubly interval censoring model. The classical approach is to use parametric families like Weibull, log-normal or gamma distributions in the estimation procedure. We propose nonparametric estimates for functions of the observations,...
journal article 2024
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Groeneboom, P. (author)
Let (Formula presented.) be the nonparametric maximum likelihood estimator of a decreasing density. Grenander characterized this as the left-continuous slope of the least concave majorant of the empirical distribution function. For a sample from the uniform distribution, the asymptotic distribution of the L<sub>2</sub>-distance of the...
journal article 2020
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Groeneboom, P. (author)
We consider smooth nonparametric estimation of the incubation time distribution of COVID-19, in connection with the investigation of researchers from the National Institute for Public Health and the Environment (Dutch: RIVM) of 88 travelers from Wuhan: Backer et al. (2020). The advantages of the smooth nonparametric approach with respect to...
journal article 2020
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Gomes, Antonio Eduardo (author), Groeneboom, P. (author), Wellner, Jon A. (author)
In carcinogenicity experiments with animals where the tumor is not palpable it is common to observe only the time of death of the animal, the cause of death (the tumor or another independent cause, as sacrifice) and whether the tumor was present at the time of death. These last two indicator variables are evaluated after an autopsy. Defining...
journal article 2019
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Groeneboom, P. (author), Hendrickx, K. (author)
Single-index models are popular regression models that are more flexible than linear models and still maintain more structure than purely nonparametric models. We consider the problem of estimating the regression parameters under a monotonicity constraint on the unknown link function. In contrast to the standard approach of using smoothing...
journal article 2018
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Groeneboom, P. (author), Jongbloed, G. (author)
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...
journal article 2018
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Groeneboom, P. (author), Hendrickx, K. (author)
We construct n-consistent and asymptotically normal estimates for the finite dimensional regression parameter in the current status linear regression model, which do not require any smoothing device and are based on maximum likelihood estimates (MLEs) of the infinite dimensional parameter. We also construct estimates, again only based on...
journal article 2018
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Groeneboom, P. (author), Hendrickx, K. (author)
It has been proved that direct bootstrapping of the nonparametric maximum likelihood estimator (MLE) of the distribution function in the current status model leads to inconsistent confidence intervals. We show that bootstrapping of functionals of the MLE can however be used to produce valid intervals. To this end, we prove that the bootstrapped...
journal article 2017
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Groeneboom, P. (author), Jongbloed, G. (author)
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,...
journal article 2015
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Groeneboom, P. (author)
journal article 2014
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Groeneboom, P. (author), Ketelaars, T. (author)
We study three estimators for the interval censoring case 2 problem, a histogram-type estimator, the maximum likelihood estimator (MLE) and the smoothed MLE, using a smoothing kernel. Our focus is on the asymptotic distribution of the estimators at a fixed point. The estimators are compared in a simulation study.
journal article 2011
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Groeneboom, P. (author), Jongbloed, G. (author), Witte, B.I. (author)
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...
journal article 2010
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Groeneboom, P. (author), Maathuis, M.H. (author), Wellner, J.A. (author)
We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” Both types of estimators were studied by Jewell, van der Laan and Henneman [Biometrika ...
journal article 2008
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Groeneboom, P. (author), Maathuis, M.H. (author), Wellner, J.A. (author)
We study nonparametric estimation for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” Groeneboom, Maathuis and Wellner [Ann. Statist. (2008) 36 1031–1063] proved that both types of estimators converge globally...
journal article 2008
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Groeneboom, P. (author)
public lecture 2006
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Cator, E.A. (author), Groeneboom, P. (author)
We show that, for a stationary version of Hammersley’s process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North–East path L(t, t) from (0, 0) to (t, t) is equal to 2E(t ? X(t))+, where X(t) is the location of a second class particle at time t . This...
journal article 2006
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Cator, E.A. (author), Groeneboom, P. (author)
We show that, for a stationary version of Hammersley’s process, with Poisson “sources” on the positive x-axis, and Poisson “sinks” on the positive y-axis, an isolated second-class particle, located at the origin at time zero, moves asymptotically, with probability 1, along the characteristic of a conservation equation for Hammersley’s process....
journal article 2005
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De Wolf, P.P. (author), Lopuhaa, H.P. (author), Groeneboom, P. (author)
A large part of the theory of extreme value index estimation is developed for positive extreme value indices. The best-known estimator of a positive extreme value index is probably the Hill estimator. This estimator belongs to the category of moment estimators, but can also be interpreted as a quasi-maximum likelihood estimator. It has been...
journal article 2003
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Groeneboom, P. (author), Jongbloed, G. (author), Wellner, J.A. (author)
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...
journal article 2001
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Groeneboom, P. (author), Jongbloed, G. (author), Wellner, J.A. (author)
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...
journal article 2001
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