SiZer for time series: A new approach to the analysis of trends

Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are `really there' and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish `trend' from `dependence'. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.Comment: Published at http://dx.doi.org/10.1214/07-EJS006 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Muon anomalous magnetic moment from effective supersymmetry

We present a detailed analysis on the possible maximal value of the muon (g-2) (= 2 a_mu) within the context of effective SUSY models with R parity conservation. First of all, the mixing among the second and the third family sleptons can contribute at one loop level to the a_mu(SUSY) and tau -> mu gamma simultaneously. One finds that the a_mu(SUSY) can be as large as (10-20)*10^-10 for any tan beta, imposing the upper limit on the tau -> mu gamma branching ratio. Furthermore, the two-loop Barr-Zee type contributions to a_mu(SUSY) can be significant for large tan beta, if a stop is light and mu and A_t are large enough (O(1) TeV). In this case, it is possible to have a_mu(SUSY) upto O(10)*10^-10 without conflicting with tau -> l gamma. We conclude that the possible maximal value for a_mu(SUSY) is about 20*10^-10 for any tan beta. Therefore the BNL experiment on the muon a_mu can exclude the effective SUSY models only if the measured deviation is larger than \sim 30*10^-10.Comment: 10 pages, 3 figure