https://hdl.handle.net/10419/177 2026-10-05T10:15:07Z 2026-10-05T10:15:07Z Wied, Dominik Weißbach, Rafael https://hdl.handle.net/10419/39692 2023-11-27T02:49:51Z 2010-01-01T00:00:00Z

Title: Consistency of the kernel density estimator - a survey Authors: Wied, Dominik; Weißbach, Rafael Abstract: Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions is sufficient for strong consistency, proofs of exact convergence rates use deeper information about the underlying empirical processes. A unifying character, however, is that earlier and more recent proofs use bounds on the probability that a sum of random variables deviates from its mean.

2010-01-01T00:00:00Z Dette, Holger Pepelyshev, Andrey Shpilev, Piter Wong, Weng Kee https://hdl.handle.net/10419/36591 2023-11-10T02:09:19Z 2009-01-01T00:00:00Z

Title: Optimal designs for estimating critical effective dose under model uncertainty in a dose response study Authors: Dette, Holger; Pepelyshev, Andrey; Shpilev, Piter; Wong, Weng Kee Abstract: Toxicologists have been increasingly using a class of models to describe a continuous response in the last few years. This class consists of nested nonlinear models and is used for estimating various parameters in the models or some meaningful function of the model parameters. Our work here is the first to address design issues for this popular class of models among toxicologists. Specifically we construct a variety of optimal designs under model uncertainty and study their properties for estimating the critical effective dose (CED), which is model dependent. Two types of optimal designs are proposed: one type maximizes the minimum of efficiencies for estimating the CED regardless which member in the class of models is the appropriate model, and (ii) dual-objectives optimal design that simultaneously selects the most appropriate model and provide the best estimates for CED at the same time. We compare relative efficiencies of these optimal designs and other commonly used designs for estimating CED. To facilitate use of these designs, we have constructed a website that practitioners can generate tailor-made designs for their settings.

2009-01-01T00:00:00Z Fokianos, Konstantions Fried, Roland https://hdl.handle.net/10419/41051 2023-11-13T02:18:39Z 2009-01-01T00:00:00Z

Title: Interventions in ingarch processes Authors: Fokianos, Konstantions; Fried, Roland Abstract: We study the problem of intervention effects generating various types of outliers in a linear count time series model. This model belongs to the class of observation driven models and extends the class of Gaussian linear time series models within the exponential family framework. Studies about effects of covariates and interventions for count time series models have largely fallen behind due to the fact that the underlying process, whose behavior determines the dynamics of the observed process, is not observed. We suggest a computationally feasible approach to these problems, focusing especially on the detection and estimation of sudden shifts and outliers. To identify successfully such unusual events we employ the maximum of score tests, whose critical values in finite samples are determined by parametric bootstrap. The usefulness of the proposed methods is illustrated using simulated and real data examples.

2009-01-01T00:00:00Z Bischl, Bernd Ligges, Uwe Weihs, Claus https://hdl.handle.net/10419/36600 2023-11-04T02:06:07Z 2009-01-01T00:00:00Z

Title: Frequency estimation by DFT interpolation: a comparison of methods Authors: Bischl, Bernd; Ligges, Uwe; Weihs, Claus Abstract: This article comments on a frequency estimator which was proposed by [6] and shows empirically that it exhibits a much larger mean squared error than a well known frequency estimator by [8]. It is demonstrated that by using a heuristical adjustment [2] the performance can be greatly improved. Furthermore, references to two modern techniques are given, which both nearly attain the Cramér-Rao bound for this estimation problem.

2009-01-01T00:00:00Z