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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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Boistard, H. (author), Lopuhää, H.P. (author), Ruiz-Gazen, A. (author)
This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by Hájek (1964) and Hájek (1981) and making the remainder term more precise. Following Hájek (1981), the proof is based on Edgeworth expansions. The...
journal article 2012
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Durot, C. (author), Kulikov, V.N. (author), Lopuhaä, H.P. (author)
journal article 2012
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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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Dekking, M. (author), Simon, K. (author), Székely, B. (author)
In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor...
journal article 2011
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Castillo, I. (author), Cator, E. (author)
The problem of estimating the center of symmetry of a symmetric signal in Gaussian white noise is considered. The underlying nuisance function f is not assumed to be differentiable, which makes a new point of view to the problem necessary. We investigate the well-known sieve maximum likelihood estimators based on the cumulated periodogram, and...
journal article 2011
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Bhamidi, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)
journal article 2010
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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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Jongbloed, G. (author), Van der Meulen, F.H. (author)
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...
journal article 2009
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Ferrari, P.A. (author), Martin, J.B. (author), Pimentel, L.P.R. (author)
We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle ? of the cone: for ??180°, the direction...
journal article 2009
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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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Maas, J. (author), Van Neerven, J.M.A.M. (author)
journal article 2008
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Van der Hofstad, R. (author), Hooghiemstra, G. (author), Znamenski, D. (author)
In this paper, we study the configuration model (CM) with independent and identically-distributed (i.i.d.) degrees. We establish a phase transition for the diameter when the power-law exponent ? of the degrees satisfies ? ? (2, 3). Indeed, we show that for ? > 2 and when vertices with degree 1 or 2 are present with positive probability, the...
journal article 2007
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Cox, S. (author), Veraar, M. (author)
journal article 2007
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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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Bosma, W. (author), Dajani, K. (author), Kraaikamp, C. (author)
Expansions that furnish increasingly good approximations to real numbers are usually related to dynamical systems. Although comparing dynamical systems seems difficult in general, Lochs was able in 1964 to relate the relative speed of approximation of decimal and regular continued fraction expansions (almost everywhere) to the quotient of the...
conference paper 2006
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Kulikov, V.N. (author), Lopuhaa, H.P. (author)
journal article 2006
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Van Gaans, O. (author), Van Neerven, J. (author)
We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form
journal article 2006
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