Speaker: Dr. Augustine Wong, York University
Department of Mathematics and Statistics

Title: Overview of Likelihood-Based Inference

Abstract: Obtaining a confidence region or a performing significance test of a parameter based on the likelihood function is commonly used in statistics.  Professor Pek in last year’s presentation introduced two likelihood-based methods: Wald method (based on the maximum likelihood estimate of the parameter) and Wilks method (likelihood ratio method).  In this talk, the accuracy of these two methods is examined.  When the parameter of interest is a scalar parameter, a special way of combining the Wald method and the Wilks method is proposed.  This proposed method gives extremely accurate inference results even when the sample size is extremely small.

Suggested Readings:
          1. Barndorff-Nielsen, O.E., & Cox, D.R. (1994). Inference and Asymptotics. Chapman & Hall.
2. Bedard, M., Fraser, D.A.S., & Wong, A. (2007).  Higher accuracy for Bayesian and frequentist inference: large sample theory for small sample likelihood .  Statistical Science 22, 301-321.
3. Doganaksoy, N. & Schmee, J. (1993). Comparisons of approximate confidence intervals for distributions used in life-data analysis . Technometrics 35, 175-184.
4. Fraser, D.A.S., 1990. Tail probabilities from observed likelihoods. Biometrika 77, 65-76.
5. Fraser, D.A.S., Reid, N. & Wu, J. (1999). A simple general formula for tail probabilities for frequentist and Bayesian inference . Biometrika 86, 249-264.
6. Reid, N. (1988). Saddlepoint methods and statistical inference. Statistical Science 3, 213-238.
7. Reid, N. (1996). Higher order asymptotics and likelihood: a review and annotated bibliography . Canadian Journal of Statistics  24, 141-166.
8. Wong, A. & Wu, J. (2000).  Practical use of small sample asymptotics for distributions used in life-data analysis .  Technometrics 42, 149-155.
9. Wong, A. & Wu, J., (2001).  Approximate inference for the factor loading of a simple factor analysis model .  Scandinavian Journal of Statistics 28, 407-414.

(Note: 1, 4, 5, 6, 7 are background material, 2 is to related to Bayesian, and the rest are specific applications.)