School of Analytic Studies and Information Technology
York University
Date :
Wednesday March 5, 2003.
Time :
3:30pm
Address
Burke Science Building
Room:
138
TITLE:
Recent Likelihood Theory: Simple and Accurate Inference
Procedure
ABSTRACT:
For inference concerning the mean parameter of a normal population
involves three steps. First of all reduced the dimension of the
problem from the dimension of the data to the dimension of the
minimal sufficient statistic. Then obtain the pivotal quantity
which is free of the nuisance parameter. Finally obtain the
distribution of the pivotal quantity.
However, in practice, each of these steps may not be available.
Various asymptotic methods have been proposed to give approximate
results. In this talk, a general likelihood based asymptotic
procedure is proposed. Examples are given to illustrate the
simplicity, accuracy and generality of the proposed procedure.
The aim of this talk is to demonstrate how the methodology
can be applied and the accuracy that it can achieve. The
theoretical justification of the methodology is given in
Barndorff-Nielsen (1986, 1991) and Fraser, Reid and Wu (1999).
About the Speaker
Dr. Augustine Wong received his Ph.D. from the University of Toronto
in 1990 under the supervision of D.A.S. Fraser. Following that he held
a two year NSERC postdoctoral position at the University of Waterloo.
After a year at the University of Alberta, Dr. Wong took up a position at
York University in 1993 and became an associate professor in 1996.
Dr. Wong is currently the mathematics co-ordinator in the School
of Analytic Studies and Information Technology at York. His research
interests include statistical inference, failure data
analysis and econometrics
References
Some relevant background references will be posted here shortly.
Barndorff-Nielsen, O.E.(1986), "Inference on Full or Partial
Parameters Based on the Standardized Signed Log Likelihood
Ratio," BIOMETRIKA 73, pp. 307-322.
Fraser, D.A.S., Reid, N. & Wu, J. (1999), "A Simple General Formula
for Tail Probabilities fpr Frequentist and Bayesian Inference,"
BIOMETRIKA 86, 249-264.
Fraser, D.A.S., Wong, A. & Wu, J. (1999), "Regression Analysis,
Nonlinear or Nonnormal: Simple and Accurate p Values from
Likelihood Analysis," JOURNAL OF THE AMERICAN STATISTICAL
ASSOCIATION 94, 1286-1295.
Reid, N. (1996), "Likelihood and Higher-Order Approximations
to Tail Areas: a Review and Annotated Bibliography,"
CANADIAN JOURNAL OF STATISTICA 24, pp. 141-166.
Wong, A.C.M. & Wu, J. (2000), "Practical Small-Sample
Asymptotics for Distributions Used in Life-Data Analysis,"
TECHNOMETRICS 42, 149-155.
Wong, A.C.M. & Wu, J. (2002), "Small Sample Asymptotic
Inference for the Coefficient of Variation: Normal and
Nonnormal Models," JOURNAL OF STATISTICAL PLANNING AND
INFERENCE 104, 73-82.
Wu, J., Wong, A.C.M. & G. Jiang (2003), "Likelihood Based
Confidence Intervals for a Log-Normal Mean," STATISTICS IN
MEDICINE, to appear.
