Advances in Decision Sciences

Advances in Decision Sciences / 2007 / Article
Special Issue

Statistics and Applied Probability: A Tribute to Jeffrey J. Hunter

View this Special Issue

Research Article | Open Access

Volume 2007 |Article ID 086180 | https://doi.org/10.1155/2007/86180

Alan Lee, "On the Semiparametric Efficiency of the Scott-Wild Estimator under Choice-Based and Two-Phase Sampling", Advances in Decision Sciences, vol. 2007, Article ID 086180, 23 pages, 2007. https://doi.org/10.1155/2007/86180

On the Semiparametric Efficiency of the Scott-Wild Estimator under Choice-Based and Two-Phase Sampling

Academic Editor: Paul Cowpertwait
Received30 Apr 2007
Accepted08 Aug 2007
Published30 Oct 2007

Abstract

Using a projection approach, we obtain an asymptotic information bound for estimates of parameters in general regression models under choice-based and two-phase outcome-dependent sampling. The asymptotic variances of the semiparametric estimates of Scott and Wild (1997, 2001) are compared to these bounds and the estimates are found to be fully efficient.

References

  1. A. J. Scott and C. J. Wild, “Fitting regression models to case-control data by maximum likelihood,” Biometrika, vol. 84, no. 1, pp. 57–71, 1997. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  2. A. J. Scott and C. J. Wild, “Maximum likelihood for generalised case-control studies,” Journal of Statistical Planning and Inference, vol. 96, no. 1, pp. 3–27, 2001. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  3. C. J. Wild, “Fitting prospective regression models to case-control data,” Biometrika, vol. 78, no. 4, pp. 705–717, 1991. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  4. A. Lee, A. J. Scott, and C. J. Wild, “Fitting binary regression models with case-augmented samples,” Biometrika, vol. 93, no. 2, pp. 385–397, 2006. View at: Publisher Site | Google Scholar | MathSciNet
  5. P. J. Bickel, C. A. Klaassen, Y. Ritov, and J. A. Wellner, Efficient and Adaptive Estimation for Semiparametric Models, Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, Md, USA, 1993. View at: Zentralblatt MATH | MathSciNet
  6. N. E. Breslow, J. M. Robins, and J. A. Wellner, “On the semi-parametric efficiency of logistic regression under case-control sampling,” Bernoulli, vol. 6, no. 3, pp. 447–455, 2000. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  7. N. E. Breslow, B. McNeney, and J. A. Wellner, “Large sample theory for semiparametric regression models with two-phase, outcome dependent sampling,” The Annals of Statistics, vol. 31, no. 4, pp. 1110–1139, 2003. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  8. J. M. Robins, F. Hsieh, and W. Newey, “Semiparametric efficient estimation of a conditional density with missing or mismeasured covariates,” Journal of the Royal Statistical Society, vol. 57, no. 2, pp. 409–424, 1995. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  9. B. McNeney and J. A. Wellner, “Application of convolution theorems in semiparametric models with non-i.i.d. data,” Journal of Statistical Planning and Inference, vol. 91, no. 2, pp. 441–480, 2000. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  10. P. J. Bickel and J. Kwon, “Inference for semiparametric models: some questions and an answer,” Statistica Sinica, vol. 11, no. 4, pp. 863–960, 2001. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  11. W. K. Newey, “The asymptotic variance of semiparametric estimators,” Econometrica, vol. 62, no. 6, pp. 1349–1382, 1994. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  12. A. Lee and Y. Hirose, “Semi-parametric efficiency bounds for regression models under case-control sampling: the profile likelihood approach,” submitted to Annals of the Institute of Statistical Mathematics. View at: Google Scholar

Copyright © 2007 Alan Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

113 Views | 318 Downloads | 4 Citations
 PDF Download Citation Citation
 Order printed copiesOrder

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.