Friday, June 26, 2009

#67. Old paper by Colubi et al.

A survey on fuzzy random variables from the point of view of Statistics.

Ana Colubi, Renato Coppi, Pierpaolo D'Urso, María Ángeles Gil (2007). Statistics with fuzzy random variables. Metron 65, 277-303.

It gives a good overview of what the Oviedo group has been doing for many years now, anyway I feel the survey is maybe too self-centered to be fair to other researchers.

Saturday, June 20, 2009

#66. Old paper by Shafer and Vovk

I presume you have heard about Glenn Shafer and Vladimir Vovk's game-theoretic approach to probability, so this one travels a different (but not really disjoint) path.

In this paper they trace the early history of measure-theoretical probability culminating in Kolmogorov's well-known book.

Glenn Shafer, Vladimir Vovk (2006). The sources of Kolmogorov’s Grundbegriffe. Statistical Science 21, 70--98.

Their account is nice and very informative, not avoiding technical details. It's a pity people don't pay historical issues more attention.

Saturday, June 06, 2009

#65. Old papers by Volker Krätschmer

You can find Krätschmer's papers here at his website.

After working for some years on fuzzy random variables and related problems, Volker, like a number of other capable researchers, recently moved on to greener pastures (probability in finance).

Specially interesting are his four papers published in 2006.

In his Test paper he discusses at length several extensions of known vector-valued integrals (Bochner and Pettis) to fuzzy random variables. The other three papers, two of them in the Journal of Multivariate Analysis, are on least squares estimation with fuzzy random variables, including "sqrt n" consistency and limit distributions, which I have never seen discussed elsewhere.