Christopher G. Small | Statistics and Actuarial Science

Professor

Department of Statistics and Actuarial Science
University of Waterloo
Waterloo, Ontario
CANADA N2L 3G1

(519) 888-4567, ext. 35541
FAX: (519) 746-1875

Email:
Office: M3 4004
Personal Website: http://www.stats.uwaterloo.ca/%7Ecgsmall/

Research and Scholarly Activity

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 twentieth 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.

Recent Refereed Papers

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.
Huang, X. and Small, C. G. (2003). Calculating the simplex median. Statistics and Computing 14, 91-98. (more)

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 in Canada, and has been team leader for Canada at various International Mathematical Olympiads including the 1998 IMO in Taipei, Taiwan; the 2001 IMO in Washington DC; 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 committee (1993--95), and is an ex-officio member of the CMS International Mathematical Olympiad 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.

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