Host Institution: |
La Trobe University, AGR Room. |
Title of Seminar: |
The Coverage Probability of Confidence Intervals in 2r factorial Experiments after Preliminary Hypothesis Testing |
Speaker's Name: |
Khageswor Giri |
Speaker's Institution: |
La Trobe University |
Time and Date: |
2:00pm Friday 23 May 2008 |
Seminar Abstract: |
We consider a 2r factorial experiment with at least two replicates. Our aim is to find a confidence interval for θ, a specified linear combination of regression parameters. We suppose that preliminary hypothesis tests are carried out sequentially beginning with the rth order interaction. After these preliminary hypothesis tests, a confidence interval for θ with nominal coverage 1-α is constructed under the assumption that the selected model is given to us a priori. We call this the naïve 1-α confidence interval for θ. We describe a new efficient Monte Carlo method, which employs conditioning for variance reduction, for estimating the minimum coverage probability of the naive confidence interval. The application of this method is demonstrated in the context of a 23 factorial experiment with 2 replicates and a particular contrast θ of interest. The naive confidence interval, with nominal coverage probability 0.95, has minimum coverage probability that is, to a good approximation, 0.464. This shows that the naive confidence interval is completely inadequate. |
Seminar Convenor: |
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AGR IT support: |
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