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A paradox concerning nuisance parameters and projected estimating functions

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  • Masayuki Henmi
  • Shinto Eguchi

Abstract

This paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters. In a statistical model with unknown nuisance parameters, the efficiency of an estimator of a parameter usually increases when the nuisance parameters are known. However the opposite phenomenon can sometimes occur. In this paper, we elucidate the occurrence of this paradox by examining estimating functions. In particular, we focus on the projected estimating function, which is defined by the projection of the score function on to a given estimating function. A sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters. In addition, a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators. Copyright 2004, Oxford University Press.

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  • Masayuki Henmi & Shinto Eguchi, 2004. "A paradox concerning nuisance parameters and projected estimating functions," Biometrika, Biometrika Trust, vol. 91(4), pages 929-941, December.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:929-941
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.929
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    Cited by:

    1. Masahiro Kato & Masatoshi Uehara & Shota Yasui, 2020. "Off-Policy Evaluation and Learning for External Validity under a Covariate Shift," Papers 2002.11642, arXiv.org, revised Oct 2020.
    2. Tianxi Cai & Thomas A Gerds & Yingye Zheng & Jinbo Chen, 2011. "Robust Prediction of t-Year Survival with Data from Multiple Studies," Biometrics, The International Biometric Society, vol. 67(2), pages 436-444, June.
    3. Olli Saarela & David A. Stephens & Erica E. M. Moodie & Marina B. Klein, 2015. "On Bayesian estimation of marginal structural models," Biometrics, The International Biometric Society, vol. 71(2), pages 279-288, June.
    4. Luo, Yu & Graham, Daniel J. & McCoy, Emma J., 2023. "Semiparametric Bayesian doubly robust causal estimation," LSE Research Online Documents on Economics 117944, London School of Economics and Political Science, LSE Library.
    5. Aaron L. Sarvet & Kerollos N. Wanis & Jessica G. Young & Roberto Hernandez‐Alejandro & Mats J. Stensrud, 2023. "Longitudinal incremental propensity score interventions for limited resource settings," Biometrics, The International Biometric Society, vol. 79(4), pages 3418-3430, December.
    6. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    7. Di Shu & Jessica G. Young & Sengwee Toh & Rui Wang, 2021. "Variance estimation in inverse probability weighted Cox models," Biometrics, The International Biometric Society, vol. 77(3), pages 1101-1117, September.
    8. Han, Chirok & Kim, Beomsoo, 2011. "A GMM interpretation of the paradox in the inverse probability weighting estimation of the average treatment effect on the treated," Economics Letters, Elsevier, vol. 110(2), pages 163-165, February.
    9. Hitomi, Kohtaro & Nishiyama, Yoshihiko & Okui, Ryo, 2008. "A Puzzling Phenomenon In Semiparametric Estimation Problems With Infinite-Dimensional Nuisance Parameters," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1717-1728, December.
    10. John Copas & Shinto Eguchi, 2010. "Likelihood for statistically equivalent models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 193-217, March.
    11. Prokhorov, Artem & Schmidt, Peter, 2009. "GMM redundancy results for general missing data problems," Journal of Econometrics, Elsevier, vol. 151(1), pages 47-55, July.
    12. Li-Pang Chen & Grace Y. Yi, 2021. "Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 481-517, June.

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