Spin Effects in High Energy Fragmentation Processes

Recent measurements, in particular those on $\Lambda$ polarization and spin alignment of vector mesons in $e^+e^-$ annihilation at LEP, and those on the azimuthal asymmetry at HERA, have attracted much attention on the spin effects in high energy fragmentation processes. In this talk, we make a brief introduction to the different topics studied in this connection and a short summary of the available data. After that, we present a short summary of the main theoretical results that we obtained in studying these different topics. The talk was mainly based on the publications [5-9] which have been finished in collaboration with C.Boros, Liu Chun-xiu and Xu Qing-hua.Comment: Plenary talk given at the 3rd Circum-Pan-Pacifc Symposium on High Energy Spin Physics, October 2001, 8 pages, 4 figure

Multidimensional trimming based on projection depth

As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators. It is found that the projection depth trimmed means are highly robust locally as well as globally. Asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions. The strong consistency, asymptotic representation and limiting distribution of the depth trimmed means are obtained. Relative to the mean and other leading competitors, the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated. Simulation studies confirm the validity of the asymptotic efficiency results at finite samples.Comment: Published at http://dx.doi.org/10.1214/009053606000000713 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org