Welcome to my home page. I am a Professor in the Department of Statistics and Actuarial Science, with interests in the foundations of statistical inference (including estimating functions and function space methods in statistics), stochastic geometry and the statistical theory of shape.
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C. G. Small (2010). Expansions and Asymptotics for Statistics. Monographs in Statistics and Applied Probability 115. CRC Press.
C. G. Small (2007). Functional Equations and How to Solve Them. Published in Springer Problem Books in Mathematics.
C. G. Small and Jinfang Wang (2003) Numerical Methods for Nonlinear Estimating Equations. . Published in Oxford Statistical Science Series.
C. G. Small (1996). The Statistical Theory of Shape. In the Springer Series in Statistics.
Multivariate Analysis of Data in Curved Shape Spaces Slides from a talk given at the Fields Institute at the International Workshop on Perspectives in High Dimensional Data Analysis (IWPHDA) in June 2011.
Dynamic Random Graph Modelling and Applications in the UK 2001 Foot-and-Mouth Epidemic. Slides from a talk given at the Winter Meeting of the Canadian Mathematical Society in December 2009 in Windsor, Ontario. The paper, which is joint work with Yasaman Hosseinkashi and Shoja Chenouri, has a self-explanatory title. The basic idea is to use a Markov chain whose state space is collection of planar graphs with directed edges. The vertices of the graph are farms where the FMD outbreak occurred, and the directed edges are the (unobserved) paths of disease contamination from one farm to another. The power point slides are here.
Cockroaches and Thylacines. Slides from a talk given in Tasmania in August 2008. In the talk I examine some statistical questions about species extinction from the fossil record. The talk also includes some statistical analysis of population decline for the thylacine in early twentieth century Tasmania.
The 1998 International Mathematical Olympiad. Since 1995, I have been working in one capacity or another as a Canadian representative to the International Mathematical Olympiad. This brief report on the 1998 IMO, when I was Leader for the Canadian team, does not stand on its own. However, for those interested in mathematics competitions, this report provides some idea of the personal side of training for such an event.
While on that trip I gave a talk on "The Statistical Analysis of Dynamic Curves and Sections" at the Institute for Statistical Mathematics in Tokyo. ( PS and PDF) This talk was also given at the University of Florida, January 11-12, 2002 at the IMS Winter Workshop on Imaging, Classification and Clustering.
In 2007 at the University of Guelph, I gave a talk on the estimation of covariance kernels for nonstationary processes. Here are the slides. (PDF)
More training materials for the
IMO. IN this case some problem sets for the 2009 IMO summer training
camp at Banff, Alberta.
Games and Strategies (PDF)
Offbeat Geometry Problems (PDF)
The Rearrangement Inequality and Consequences (PDF).
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