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http://hdl.handle.net/2451/31541
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| Title: | Minimax and the Value of Information |
| Authors: | Sadler, Evan |
| Issue Date: | 18-Apr-2012 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | ;SOR-2012-01 |
| Abstract: | In his discussion of minimax decision rules, Savage (1954, p. 170)
presents an example purporting to show that minimax applied to negative
expected utility (referred to by Savage as 'negative income') is an
inadequate decision criterion for statistics; he suggests the
application of a minimax regret rule instead. The crux of Savage's
objection is the possibility that a decision maker would choose to
ignore even 'extensive' information. More recently, Parmigiani (1992)
has suggested that minimax regret suffers from the same flaw. He
demonstrates the existence of 'relevant' experiments that a minimax
regret agent would never pay a positive cost to observe. On closer
inspection, I find that minimax regret is more resilient to this
critique than would first appear. In particular, there are cases where
no experiment has any value to an agent employing the minimax negative
income rule, while we may always devise a hypothetical experiment that a
minimax regret agent would pay for. The force of Parmigiani's critique
is further blunted by the observation that 'relevant' experiments exist
for which a Bayesian agent would never pay. I conclude by discussing the
notion of pessimism in the context of minimax decision rules. |
| URI: | http://hdl.handle.net/2451/31541 |
| Appears in Collections: | IOMS: Statistics Working Papers
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