Displaying similar documents to “On optimality of the LR tests in the sense of exact slopes. I. General case”

A Bimodality Test in High Dimensions

Palejev, Dean (2012)

Serdica Journal of Computing

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We present a test for identifying clusters in high dimensional data based on the k-means algorithm when the null hypothesis is spherical normal. We show that projection techniques used for evaluating validity of clusters may be misleading for such data. In particular, we demonstrate that increasingly well-separated clusters are identified as the dimensionality increases, when no such clusters exist. Furthermore, in a case of true bimodality, increasing the dimensionality makes identifying...

Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds, Petr Gurka, Bohumír Opic (1995)

Studia Mathematica

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This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.