Papers by Helmut Strasser
Lecture notes in statistics, 1985
Let T: = {0,1,2,..., k}. An experiment E = (Ω, A, {Po,P1,..., Pk}) for the parameter space T is a... more Let T: = {0,1,2,..., k}. An experiment E = (Ω, A, {Po,P1,..., Pk}) for the parameter space T is abbreviated by E = (Po,P1,..., Pk).
Bulletin of The London Mathematical Society, May 1, 1992
Lecture notes in statistics, 1985
Springer eBooks, 1985
ABSTRACT
Lecture notes in statistics, 1985
Let T ≠ O. If E = (Ω, A, {Pt: t ∈ T}) is an experiment for the parameter space T and c > 0, we... more Let T ≠ O. If E = (Ω, A, {Pt: t ∈ T}) is an experiment for the parameter space T and c > 0, we may consider the random experiment which consists in first selecting a sample size n ∈ℕ0 according to a Poisson variable with expectation c and then carrying out the n-fold direct product (Ωn, An, {Ptn : t ∈ T)) of E. (Here Ω0 consists of a single point.) This experiment can be described as follows. As sample space take the direct sum (\( \underset{n=0}{\overset{\infty }{\mathop \oplus }}\,{{\Omega }^{n}},\underset{n=0}{\overset{\infty }{\mathop \oplus }}\,{{A}^{n}} \)), the underlying set of probability measures is {e(c Pt): t ∈ T), the normalized exponential of any finite measure μ on A being defined by $$ \varepsilon (\mu ):={{e}^{-\mu (\Omega )}}\underset{n=0}{\overset{\infty }{\mathop \oplus }}\,\frac{{{\mu }^{n}}}{n!} $$
Lecture notes in statistics, 1985
In this section we shall characterize the weak convergence of Poisson experiments in terms of the... more In this section we shall characterize the weak convergence of Poisson experiments in terms of the convergence of the associated Levy measures, thus obtaining a general representation of the Hellinger transforms of the possible limit experiments. Some of the following results are obviously known and used by LeCam, 1974 (Sec. 9), but not all of them are stated and proved there. The exposition will be given for nets instead of sequences, as the space of experiment-types is weakly compact (LeCam, 1974, p. 29) but in general not weakly sequentially compact. Moreover, nets will be needed in the third part.
Lecture notes in statistics, 1985
Statistics and Risk Modeling, 2001
The paper deals with a class of quantization problems and algorithms based on partitions of R d w... more The paper deals with a class of quantization problems and algorithms based on partitions of R d which are defined by maximal support planes (MSP) of a convex function. This kind of problems generalizes the well-known minimum variance partition problem of statistical cluster analysis. The extension is a multivariate version of the topic considered by Bock, [4]. It is basically different from those kinds of quantization problems which have been considered by Pollard, [15], and Pärna, [14], and which are called principal point problems by Flury, [7]. As a side result it is shown that some competitive learning problems considered by Kohonen, [10], belong to the class considered in this paper. The paper contains theoretical results like existence of optima, consistency of approximate optima and characterization of local optima as fixpoints of a fixpoint algorithm. A fix point algorithm is proposed and its termination after finite time is proved for empirical distributions. Modifying the underlying convex function gives room for a large variety of new classification procedures, e.g., of robust quantifiers. Several examples are discussed by way of illustration. Numerical studies of the performance of such procedures are the subject of the Doctoral Thesis by Steiner,
Lecture notes in statistics, 1985
Lecture notes in statistics, 1985
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Papers by Helmut Strasser