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- Norbert Gaffke, Friedrich Pukelsheim
- Mathematical Social Sciences
- 2008

When the seats in a parliamentary body are to be allocated proportionally to some given weights, such as vote counts or population data, divisor methods form a prime class to carry out the apportionment. We present a new characterization of divisor methods, via primal and dual optimization problems. The primal goal function is a cumulative product of the… (More)

- Norbert Gaffke, Friedrich Pukelsheim
- Math. Meth. of OR
- 2008

The problems of (bi-)proportional rounding of a nonnegative vector or matrix, resp., are written as particular separable convex integer minimization problems. Allowing any convex (separable) objective function we use the notions of vector and matrix apportionment problems. As a broader class of problems we consider separable convex integer minimization… (More)

- Meik Dörpinghaus, Norbert Gaffke, Lorens A. Imhof, Rudolf Mathar
- 2013 Information Theory and Applications Workshop…
- 2013

In the present work, a discrete-time stationary Rayleigh flat-fading channel with unknown channel state information at the transmitter and the receiver is considered. The law of the channel is assumed to be known at the receiver and the fading process is supposed to be a stationary Gaussian process with an absolutely summable autocorrelation function. The… (More)

- Karl Heinz Borgwardt, Norbert Gaffke, Michael Jünger, Gerhard Reinelt
- Applied Geometry And Discrete Mathematics
- 1990

- Norbert Gaffke, Ulrike Graßhoff, Rainer Schwabe
- Computational Statistics & Data Analysis
- 2014

- Jörg Budde, Norbert Gaffke
- Math. Meth. of OR
- 1999

The cost minimization problem in an agency model with imperfect monitoring is considered. Under the ®rst order approach, this can be stated as a convex minimization problem with linear inequality and equality constraints in a generally in®nite dimensional function space. We apply the Fenchel Duality Theorem, and obtain as a dual problem a concave… (More)

- Meik Dörpinghaus, Norbert Gaffke, Lorens A. Imhof, Rudolf Mathar
- SIAM J. Matrix Analysis Applications
- 2015

We prove a new inequality for the expectation E [log det (WQ+ I)], where Q is a nonnegative definite matrix and W is a diagonal random matrix with identically distributed nonnegative diagonal entries. A sharp lower bound is obtained by substituting Q by the diagonal matrix of its eigenvalues Γ. Conversely, if this inequality holds for all Q and Γ, then the… (More)

- Norbert Gaffke
- 2004

We consider the nonparametric model of n i. i. d. nonnegative real random variables whose distribution is unknown. An interesting parameter of that distribution is its expectation μ. Wang & Zhao (2003) studied the problem of testing the one-sided hypotheses H0 : μ ≤ μ0 vs. H1 : μ > μ0 (with a given μ0 > 0, where w.l.g. one may take μ0 = 1). For n = 1 there… (More)

- Moudar Soumaya, Norbert Gaffke, Rainer Schwabe
- J. Multivariate Analysis
- 2015

The concept of seemingly unrelated models is used for multivariate observations when the components of the multivariate dependent variable are governed by mutually different sets of explanatory variables and the only relation between the components is given by a fixed covariance within the observational units. A multivariate weighted least squares estimator… (More)

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