Estimating odds and log odds with guaranteed accuracy

Luis Mendo ()
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Luis Mendo: Universidad Politécnica de Madrid

Statistical Papers, 2025, vol. 66, issue 1, No 26, 17 pages

Abstract: Abstract Two sequential estimators are proposed for the odds $$p/(1-p)$$ p / ( 1 - p ) and log odds $$\log (p/(1-p))$$ log ( p / ( 1 - p ) ) respectively, using independent Bernoulli random variables with parameter p as inputs. The estimators are unbiased, and guarantee that the variance of the estimation error divided by the true value of the odds, or the variance of the estimation error of the log odds, are less than a target value for any $$p \in (0,1)$$ p ∈ ( 0 , 1 ) . The estimators are close to optimal in the sense of Wolfowitz’s bound.

Keywords: Estimation; Odds; Log odds; Mean-square error; Efficiency; 62F10; 62L12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-024-01639-w

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