Christopher Small

Christopher Small's personal website

Research interests

Professor Small's research interests are in statistical inference, including estimating functions; and some areas of statistical geometry, including the statistical analysis of shape. Recently, he has been working on a book on asymptotic techniques.

Over the last two decades, the statistical analysis of shape has become a key technique for the study of computer vision and pattern recognition, including data from satellite images and computer tomography. To analyze such images, points called "landmarks" are extracted as a summary of the important geometrical information in the image. Medical researchers and clinicians now routinely use landmarks as a means for encoding image information. A set of landmarks obtained in this way from an image is called a configuration, and is usually represented as a matrix of coordinates. From such matrices, information about the shape of the landmarks is then extracted, where the shape of a configuration is defined to be the sum total of all landmark image information that is independent of the choice of coordinate frame of the unit of measurement.

Statistical asymptotics can be roughly defined as the study of the properties of statistics for large samples. Often, the determination of an optimal or efficient statistical method depends upon consideration of its behaviour for such large samples, where comparisons between methods become clearer. The field of asymptotics was initiated by Henri Poincare in mathematical analysis and was adapted to statistics early in the 20th century by researchers such as Wilks, Cramer, Aitken, and Rao. In recent years symbolic computing packages such as Maple have opened up new possibilities for implementing many of these ideas, which were too laborious to work out before. Professor Small is particularly interested in implementing the use of Pad\'e approximants for asymptotic likelihood inference.

Education/biography

Professor Small is a member of a number of academic organizations, including the Institute of Mathematical Statistics, the Royal Statistical Society, the Canadian Mathematical Society, and the Statistical Society of Canada.

He served on the board of directors for the 1995 International Mathematical Olympiad (IMO) in Canada, and has been team leader for Canada at various IMOs including the 1998 IMO in Taipei, Taiwan; the 2001 IMO in Washington, D.C.; and the 2004 IMO in Athens, Greece. He also served as deputy leader for the Canadian team at the IMO in South Korea.

He has served on various national committees for the Canadian Mathematical Society including the Canadian Mathematical Olympiad (CMS) committee (1993-95), and is an ex-officio member of the CMS IMO committee.

Professor Small was also a member of the international advisory board for Chiba University for 1999-2000, and a member of the systematic program review team for the Department of Mathematics and Statistics at the University of Saskatchewan.

Selected publications

• Chenouri, S. and Small, C. G. (2012). A nonparametric multivariate multisample test based on data depth. Accepted for Electronic J. Statist.
• Hosseinkashi, Y., Chenouri, S., Small, C. G. and Deardon, R. (2012). A stochastic graph process for epidemic modelling. Can. J. Statist. 40, 55--67.
• Small, C. G. (2011).  Statistics of shape. Wiley Interdisc. Rev.:  Comp. Statist. 3, 428--433, doi: 10.1002/wics.173.
• Chenouri, S., Small, C. G. and  Farrar, T. J. (2011). Data depth-based nonparametric scale tests. Can. J. Statist. 39, 356--369.
• Small, C. G. (2010). Expansions and Asymptotics for Statistics. Chapman and Hall/CRC Monographs on Statistics and Applied Probability, 343+xiv pages.
• Heo, G. and Small, C. G. (2006).  Form representations and form averages: a survey and comparative study. Computer Vision and Image Understanding 102, 188-203.
• Small, C. G. (2006).  Functional Equations and How to Solve Them. Springer Problem Books in Mathematics, Springer, New York, 141 pages.
• Small, C.G. and Wang, J. (2003). Numerical Methods for Nonlinear Estimating Equations. Oxford University Press, 310 pages.
• Small, C.G. (1996). The Statistical Theory of Shape. Springer, New York, 227 pages. Reviewed in:  Zentralblatt fuer Mathematik und ihre Grenzgebiete 859.1997, S. 395.  Also reviewed in Short Book Reviews Vol. 17, p. 4.
• Small, C.G. and McLeish, D.L. (1994). Hilbert Space Methods in Probability and Statistical Inference. Wiley, New York, 252 pages. Reviewed in: J. Amer. Statist. Assoc. 1995, pp. 1491-1492. Also reviewed in Short Book Reviews Vol 14, p. 47.