184
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Sampling and empirical risk minimization

, &
Pages 30-42 | Received 25 May 2016, Accepted 26 Sep 2016, Published online: 14 Dec 2016

References

  • Horvitz DG, Thompson DJ. A generalization of sampling without replacement from a finite universe. JASA. 1951;47:663–685.
  • Berger YG. Rate of convergence to normal distribution for the Horvitz-Thompson estimator. J Statist Plann Inference. 1998;67(2):209–226.
  • Deville J-C, Särndal C-E. Calibration estimators in survey sampling. JASA. 1992;87:376–382.
  • Hajek J. Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann Math Stat. 1964;35(4):1491–1523.
  • Robinson PM. On the convergence of the Horvitz-Thompson estimator. Aust J Stat. 1982;24(2):234–238.
  • Rosen P. Asymptotic theory for successive sampling. AMS. 1972;43:373–397.
  • Breslow NE, Lumley T, Ballantyne CM, et al. Improved Horvitz-Thompson estimation of model parameters from two-phase stratified samples: applications in epidemiology. Stat Biosci. 2009;1:32–49.
  • Breslow NE, Wellner JA. Weighted likelihood for semiparametric models and two-phase stratified samples, with application to Cox regression. Scand J Stat. 2007;35:186–192.
  • Breslow NE, Wellner JA. A Z-theorem with estimated nuisance parameters and correction note for ‘Weighted likelihood for semiparametric models and two-phase stratified samples, with application to Cox regression’. Scand J Stat. 2008;35:186–192.
  • Gill RD, Vardi Y, Wellner JA. Large sample theory of empirical distributions in biased sampling models. Ann Stat. 1988;16(3):1069–1112.
  • Saegusa T, Wellner J. Weighted likelihood estimation under two-phase sampling. Ann Stat. 2013;41(1):269–295.
  • Boucheron S, Bousquet O, Lugosi G. Theory of classification: a survey of some recent advances. ESAIM: Probab Stat. 2005;9:323–375.
  • Devroye L, Györfi L, Lugosi G. A probabilistic theory of pattern recognition. New York: Springer; 1996.
  • Koltchinskii V. Local Rademacher complexities and oracle inequalities in risk minimization (with discussion). Ann Stat. 2006;34:2593–2656.
  • Clémençon S, Bertail P, Chautru E. Scaling-up M-estimation via sampling designs: the Horvitz-Thompson stochastic gradient descent. Proceedings of the 2014 IEEE International Conference on Big Data; Washington, USA; 2014.
  • Bottou L, Bousquet O. The trade-offs of large-scale learning. In: Platt J, Koller D, Singer Y, Roweis S, editors. Advances in neural information processing systems 20. Proceedings of NIPS'07; Vancouver, B.C., Canada; 2008. p. 161–168.
  • Steinwart I, Hush D, Scovel C. Learning from dependent observations. J Multivariate Anal. 2009;100(1):175–194.
  • Agarwal A, Duchi JC. The generalization ability of online algorithms for dependent data. IEEE Trans Inf Theory. 2013;59(1):573–587.
  • Cochran W. Sampling techniques. New York: Wiley; 1977.
  • Deville J. Réplications d'échantillons, demi-échantillons, Jackknife, bootstrap dans les sondages. Economica, Ed. Droesbeke, Tassi, Fichet; 1987.
  • Särndal C, Swensson B, Wretman J. Model assisted survey sampling. New York: Springer-Verlag; 1992. (Springer Series in Statistics).
  • Bartlett PL, Jordan MI, McAuliffe JD. Convexity, classification, and risk bounds. J Am Statist Assoc. 2006;101(473):138–156.
  • Bertail P, Chautru E, Clémençon S. Empirical processes in survey sampling with (conditional) poisson designs. Submitted to the Scand J Stat. 2016. DOI:10.1111/sjos.12243
  • Clémençon S, Bertail P, Chautru E, et al. Survey schemes for stochastic gradient descent with applications to M-estimation. Submitted for publication. Available from: http://arxiv.org/abs/1501.02218
  • van der Vaart A, Wellner J. Weak convergence and empirical processes. New York: Springer; 1996.
  • Tsybakov A. Introduction à l'estimation non-paramétrique. New York: Springer; 2004. (Mathématiques et Applications).
  • Lugosi G, Zeger K. Concept learning using complexity regularization. IEEE Trans Inf Theory. 1996;42:48–54.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.