My research interests include empirical likelihood, model/variable selection, and group effects of predictor variables in regression models. I developed an extended empirical likelihood which generalizes the original empirical likelihood to the full parameter space while preserving its geometric characteristics. This extended empirical likelihood is substantially more accurate than the original empirical likelihood. I devised a constrained minimum criterion (CMC) for selecting regression models using the log-likelihood ratio of a model instead of a penalized log-likelihood. The CMC is a frequentist alternative and a strong competitor to the AIC and BIC for selecting regression models. For strongly correlated predictor variables in linear models, I introduced group effects to capture their collective impact on the response variable. Meaningful group effects can be accurately estimated, and they characterize the region in the predictor variable space over which predictions by the least squares estimated model are accurate. I also proposed a group least squares regression for handling the multicollinearity problem associated with such variables which is superior to existing solutions such as the ridge regression and principal component regression.

Interests

• Empirical likelihood
• Model/variable selection
• Group effects in linear models
• Saddlepoint approximation
• Applied statistics

Courses

• Fall 2024: 听 听
• Spring 2025:
• Summer 2025:

Selected Publications

• Tsao, M. (2023) Regression model selection via log-likelihood ratio and constrained minimum criterion. Canadian Journal of Statistics, .
• Tsao, M. (2022) Group least squares regression for linear models with strongly correlated predictor variables, Annals of Institute of Statistical Mathematics, :.
• Tsao, M. (2021) A constrained minimum criterion for model selection, Stat, 10(1), e387.
• Tsao, M. (2019) Estimable group effects for strongly correlated variables in linear models, Journal of Statistical Planning and Inference, 198, 29-42.
• Tsao, M. and Wu, F. (2013) Empirical likelihood on full parameter space, Annals of Statistics, 41, 2176-2196.
• Tsao, M. (2004) Bounds on coverage probabilities of the empirical likelihood ratio confidence regions, Annals of Statistics, 32, 1215-1221.