On a paradox in decision-theoretic interval estimation

Host Institution:

La Trobe University

Title of Seminar:

On a paradox in decision-theoretic interval estimation

Speaker's Name:

Assoc. Prof. Paul Kabaila

Speaker's Institution:

La Trobe University

Time and Date:

Friday 5 October, 11.00 AM (EST)

Seminar Abstract:

Confidence intervals are assessed according to two criteria, namely expected
length and coverage probability. In an attempt to apply the decision-theoretic method to finding a good confidence interval, a loss function that is a linear combination of the interval length and the indicator function that the interval includes the parameter of interest has been proposed. We consider the particular case that the parameter of interest is the normal mean, when the variance is unknown. Casella, Hwang and Robert (1993) have shown that this loss function, combined with the standard noninformative prior, leads to a generalised Bayes rule that is a confidence interval for this parameter which has ``paradoxical behaviour''. We show that a simple modification of this loss function, combined with the same prior, leads to a generalized Bayes rule that is the usual confidence interval i.e. the ``paradoxical behaviour'' is removed.

References
Casella, G., Hwang, J.T.G. and Robert, C. (1993). A paradox in decision-theoretic interval estimation. Statistica Sinica, 3, 141-155.
Kabaila, P. (2012). Note on a paradox in decision-theoretic interval estimation. To appear in Statistics & Probability Letters.

Seminar Convenor:

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AGR IT support:

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