Christopher Small

Biography

Dr. Christopher Small is a professor in the Department of Statistics and Actuarial Science, University of Waterloo, University Avenue West, Waterloo, ON, Canada.

Research Interest

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.