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SPEAKER: |
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TITLE: |
"Measuring Information When Fisher's Fails" |
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DAY: |
Wednesday, October 27, 1999 |
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TIME: |
3:30 p.m. [Coffee in BSB-202 at 3:00 p.m.] |
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PLACE: |
BSB-108 |
Fisher's information measure and its relationship with the problem of best estimation is very well known. However, there are many situations where the Fisher information can not be determined as the likelihood function is not differentiable with respect to the parameter. In this case, I will discuss a simple linear sensitivity measure (discussed earlier by Tukey) and explain how it can be computed, and what its relationship to the problem of best estimation is.
In the second part of the lecture, I will propose a multiparameter version of this information measure and prove some of its properties including non-negative definiteness, weak additivity, monotonicity and convexity. I will point out its relationship to the Fisher information (when we can determine it) and the Best Linear Unbiased Estimation of parameters. Finally, I will present some illustrative examples.
Dr. Balakrishnan is a Professor in the Department of Mathematics and Statistics at McMaster University. His research interests include Order Statistics, Inferential Methods, Distribution Theory, Life-testing and Reliability, Multivariate Analysis and Robust Inference. He is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute. Dr. Balakrishnan is on the editorial board of many journals including Communications in Statistics, Naval Research Logistics and Computational Statistics & Data Analysis.
The reference below, which Dr. Balakrishnan has provided as useful background for his talk, has been placed on reserve at Thode Library (STATS 770: Statistics Seminar).
[1] Arnold, B.C., Balakrishnan, N. & Nagaraja, H.N. (1992), A FIRST COURSE IN ORDER STATISTICS, Wiley: New York, pp. 162-167.