Internet: Announcement

Leader	Cheolwoo Park (SAMSI), cwpark@email.unc.edu
Meeting	Thursday 1:00 - 2:00 pm, room 203
Members	Fred Godtliebsen (University of Tromso, Norway), godtlieb@email.unc.edu Arka Ghosh (University of North Carolina, Chapel Hill), apghosh@email.unc.edu Juhyun Park (University of North Carolina, Chapel Hill), parkj@email.unc.edu Stilian Stoev (Boston University), sstoev@bu.edu Murad Taqqu (Boston University), murad@bu.edu
Outline Objectives	In an analysis of long range dependent time series, a Logscale Diagram using a wavelet method is quite useful. Logscale Diagram is essentially a log-log plot of variance estimates of the wavelet details at each scale, against scale, complete with confidence intervals about these estimates at each scale. It can be thought of as a spectral estimator where large scale corresponds to low frequency. For example, one can estimate the Hurst Parameter from a Logscale Diagram by applying a weighted least square fit for a certain range of scales. SiZer enables meaningful statistical inference, while doing exploratory data analysis using statistical smoothing methods (e.g. histograms or scatterplot smoothers). It is a new visualization that brings clear and immediate insight into a central scientific issue in exploratory data analysis: Which features observed in a smooth of data are "really there"? This central question is critical in real data analysis, because discovery of a new feature, such as an unexpected "bump" or surprising "regions of decrease/increase", might lead to important new scientific insight. One common factor of these two tools is that they are looking the data at various scales. It is worth combining these two tools and make a new one for an analysis of long range dependent time series.
Reference	- Introduction to SiZer - P. Chadhuri and J. S. Marron (1999), SiZer for exploration of structure in curves, Journal of the American Statistical Association, 94, 807-823. - V. Rondonotti and J. S. Marron, SiZer for dependent data. - Fred Godtliebsen and T.A.Oigaard, A Visual Display Device for Significant Features in Complicated Signals, Submitted. - Fred Godtliebsen, L.R. Olsen and J-G. Winther (2003), Recent developments in statistical time series analysis : Examples of use in climate research, J. Geophys. Res. 30(12), 1654-1657. - Fred Godtliebsen and L.R. Olsen, A scale-space approach for detecting changes in statistical behaviour of dependent data, Submitted. - Fred Godtliebsen, L.R. Olsen, and P. Chaudhuri, Change points in spectrum, Work in progress. - Wavelet H Estimator - P. Abry, D. Veitch (1998), Wavelet Analysis of Long Range Dependent Traffic, Trans. Info. Theory, Vol.44, No.1, 2-15. - D. Veitch, P. Abry (1999), A wavelet based joint estimator for the parameters of LRD, "Special issue on Multiscale Statistical Signal Analysis and its Applications" IEEE Trans. Info. Th. April 1999, Volume 45, No.3. - Abry, Flandrin, Taqqu, Veitch (2000), Wavelets for the analysis, estimation and synthesis of scaling data, "Self Similar Network Traffic Analysis and Performance Evaluation, K. Park and W. Willinger, Eds., Wiley. - D. Veitch, P. Abry, M. S. Taqqu, On the Automatic Selection of the Onset of Scaling.

Meetings

October 2, 2003: A brief review of SiZer and a wavelet method / Naive idea of combining these two

October 16, 2003: Description of SiZer by Fred Godtliebsen

October 30, 2003: Description of SiZer and by Fred Godtliebsen

November 6, 2003: Description of Dependent SiZer by Juhyun Park

November 13, 2003: Wavelet Spectrum by Stilian Stoev

November 20, 2003: Statistical Tools
                               Stilian Stoev (plots and movies)
                               Fred Godtliebsen
                               Cheolwoo Park

Next meeting: December 4, 2003
                      - Discussion of possible directions