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Limit theorems for out guesses with mean-guided second guessing
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- Journal:
- Journal of Applied Probability / Volume 19 / Issue 2 / June 1982
- Published online by Cambridge University Press:
- 14 July 2016, pp. 321-331
- Print publication:
- June 1982
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- Article
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A second guesser, G2, proposes to guess ‘smaller' or ‘larger' on each of n contests, i, according as
, or 
where Xi, i = 1, ···, n are the revealed guesses of the first guesser, G1. G2 wins contest i if his assertion about the size of the target quantity θ i , is more accurate than that of G1, Xi, i = 1, ···, n. Otherwise G 1 is the winner. Laws of large numbers are derived for G2's win totals for arbitrary configurations of θ i . Limiting distributions are obtained for the first guesser's win totals in two special cases, the first where the θ i are highly concentrated and the second where they are widely dispersed. G2 enjoys an enormous advantage over G1 in the former case, as intuition would suggest.
, or 
where 