Don McLeish

Research interests

Professor McLeish's research interests cover a variety of areas including probability and stochastic processes, statistical inference using estimating functions, and applications of Monte Carlo methods to finance.

More recently, he has been interested in imputing missing or incomplete data in finance and biostatistics, motivated by the fact that virtually every dataset including financial time series have related variables or cases that are only partially observed and that are often omitted as a result.

His book was published in 2005. Two invited talks on topics related to its contents were given in 2005, one to the annual meeting of the Statistical Society of Canada (SSC) in Saskatoon (June 2005) and the other to the Applied Probability meeting (INFORMS) held in Ottawa (July 2005). He has published papers on using the often disregarded distribution of the high and the low of an asset price in addition to the open and the close for estimation and testing.

Education/biography

Professor McLeish is a member of the SSC, the American Statistical Association, and the Institute of Mathematical Statistics. He has consulted with various companies in the financial services industry, and with the Ministry of Transportation of Ontario, and has organized the annual meeting of the SSC and a workshop on missing data. He has held appointments at York University, the University of Alberta, the University of Toronto, the University of Auckland, and the University of Michigan.

Professor McLeish's interest in statistical models for financial data includes the application of wide-tail alternatives to the normal distribution such as stable processes, and the consequences for derivatives and asset pricing. The application of Monte Carlo techniques, variance reduction, etc. and stochastic calculus to problems in finance are also of interest. Particularly, involving estimating the sensitivity of a simulation to the choice of underlying parameters and missing and incomplete data problems in finance. His interest in finance helped lead to the creation of the collaborative master's program in finance and the Center for Advanced Studies in Finance and the text Monte Carlo Simulation and Finance, Wiley, 2005.

Professor McLeishs's also has an interest in statistical inference, particularly applications of inference or estimating functions and related Hilbert space and projection methods in statistics. These have many interesting applications from problems involving with nuisance parameters, missing and censored data problems, inference for stochastic processes to the building of analogues of likelihood methods even when lack of a dominating measure make maximum likelihood impossible. These interests led to the book and monograph written jointly with Christopher Small.

Professor McLeish continues to work on some problems of interest in biostatistics, bioassay and experimental design, particularly sequential design for estimating extreme quantiles in bioassay and missing data problems in regression. Past work includes Central Limit Theorems and invariance principles for martingales, mixing sequences of random variables, and other dependent variables as well as martingales, their applications and inference for stochastic processes.

Selected publications

• Design and Relative Efficiency in Two-Phase Studies (2012) With Yang Zhao and J.F. Lawless. Journal of Statistical Planning and Inference (to appear)
• Statistical Modeling and the Financial Crisis (2011) In Statistics Science and Public Policy XVI. Rights, Risks and Regulations. Ed. A. M. Herzberg.
• A general method for Debiasing a Monte Carlo estimator (2011) To appear in Monte Carlo Methods Appl., 15 pages.
• McLeish, D.L. and Metzler, A. (2011) A Multiname First-Passage Model for Credit Risk. Journal of Credit Risk. 7. 1. 1-30
• A Particular Diffusion Model for Incomplete Longitudinal Data: Application to CD4 Counts and Time-to-Event Data in the Multicenter AIDS Cohort Study Biostatistics (2011) (with C.A. Struthers). Biostatistics 12 (3): 493-505.
• Comment on "option pricing under the Merton model of the short rate" (2010) (with Zhenyu Cui)  Mathematics and Computers in Simulation 81.1. 1-4
• Bounded Relative Error Importance Sampling and Rare Event Simulation (2010), ASTIN Bulletin. 40. 377-398
• Likelihood Methods for Regression Models with Expensive Variables Missing by Design (2009), (with Yang Zhao, Jerald Lawless) Biometrical Journal 51 1, 1--14
• Statistical Modeling and the Financial Crisis (2010) In Statistics Science and Public Policy XiV. Energy, Food and Water. Ed. A. M. Herzberg. 143-148