# Efficiency

Efficiency is one of the desiderata for conformal prediction and related methods. In the case of conformal predictors, efficiency means that the prediction regions should be as narrow as possible. This informal requirement can be formalized in different ways: there are various criteria of efficiency.

Fundamental results about the existence of asymptotically efficient conformal predictors have been obtained by Lei et al. (2013) and Lei and Wasserman (2014); for a summary, see, e.g., Balasubramanian et al. (2014), Sections 1.4 and 2.6.2.

**References**

- Vineeth N. Balasubramanian, Shen-Shyang Ho, and Vladimir Vovk, editors (2014).
*Conformal Prediction for Reliable Machine Learning: Theory, Adaptations, and Applications*. Morgan Kaufmann, Chennai. - Jing Lei, James Robins, and Larry Wasserman (2013). Distribution free prediction sets,
*Journal of the American Statistical Association*108:278-287. - Jing Lei and Larry Wasserman (2014). Distribution free prediction bands for nonparametric regression,
*Journal of the Royal Statistical Society B*76:71-96.