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Estimating odds and log odds with guaranteed accuracy

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  • Luis Mendo

    (Universidad Politécnica de Madrid)

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.

Suggested Citation

  • Luis Mendo, 2025. "Estimating odds and log odds with guaranteed accuracy," Statistical Papers, Springer, vol. 66(1), pages 1-17, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01639-w
    DOI: 10.1007/s00362-024-01639-w
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    References listed on IDEAS

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    1. Alan Agresti, 1999. "On Logit Confidence Intervals for the Odds Ratio with Small Samples," Biometrics, The International Biometric Society, vol. 55(2), pages 597-602, June.
    2. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
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