Eckhard Liebscher

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In this paper we introduce two methods for the construction of asymmetric multivariate copulas. The …rst is connected with products of copulas. The second approach generalises the Archimedean copulas. The resulting copulas are asymmetric and may have more than two parameters in contrast to most of the parametric families of copulas described in the(More)
In this paper we derive rates of strong convergence for the kernel density estimator and for the Nadaraya-Watson estimator under the-mixing condition and under the condition of absolute regularity. A combination of an inequality of Bernstein type (Rio 1995) and an exponential inequality (cf. Fuk/Nagaev 1971) is the crucial tool for the proofs. Moreover, we(More)
Assume that C1, . . . , Ck : [0, 1]d → [0, 1] are copulas. Let gji : [0, 1] → [0, 1] for j = 1, . . . , k, i = 1, . . . , d be functions with the property that each of them is strictly increasing or is identically equal to 1. Suppose that ∏k j=1 gji(v) = v for v ∈ [0, 1], i = 1, . . . , d, and limv→0+0 gij(v) = gji(0) for j = 1, . . . , k, i = 1, . . . , d.(More)
In this paper we prove rates of uniform strong convergence, convergence rates of the mean square error and the asymptotic normality of the kernel estimator for the transition density of a geometrically ergodic Markov chain. The assumptions on the Markov chain are closely related to absolute regularity. We allow the initial distribution of the Markov chain(More)
Abstract: Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius(More)
This paper describes a statistical procedure working on ultrasound B-mode images that were recorded with the transducer array radiating in air. From the digital image data, a gray value profile was generated using a computer program. A statistical procedure was developed to examine if there are significant deviations from the mean. They occur, for example,(More)
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