17,138 research outputs found
A cautionary note on robust covariance plug-in methods
Many multivariate statistical methods rely heavily on the sample covariance
matrix. It is well known though that the sample covariance matrix is highly
non-robust. One popular alternative approach for "robustifying" the
multivariate method is to simply replace the role of the covariance matrix with
some robust scatter matrix. The aim of this paper is to point out that in some
situations certain properties of the covariance matrix are needed for the
corresponding robust "plug-in" method to be a valid approach, and that not all
scatter matrices necessarily possess these important properties. In particular,
the following three multivariate methods are discussed in this paper:
independent components analysis, observational regression and graphical
modeling. For each case, it is shown that using a symmetrized robust scatter
matrix in place of the covariance matrix results in a proper robust
multivariate method.Comment: 24 pages, 7 figure
A small tabletop experiment for a direct measurement of the speed of light
A small tabletop experiment for a direct measurement of the speed of light to
an accuracy of few percent is described. The experiment is accessible to a wide
spectrum of undergraduate students, in particular to students not majoring in
science or engineering. The experiment may further include a measurement of the
index of refraction of a sample. Details of the setup and equipment are given.
Results and limitations of the experiment are analyzed, partly based on our
experience in employing the experiment in our student laboratories. Safety
considerations are also discussed.Comment: 4pages, 5fig
On the eigenvalues of the spatial sign covariance matrix in more than two dimensions
Acknowledgments Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.Non peer reviewedPostprin
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