Expectiles are a class of summary statistics generalising the expected value [1, 2]. They have been relatively neglected since their introduction [3]. Perhaps this is because they lacked a simple calculation procedure and an immediate interpretation like that of the expected value or that of quantiles.
See derivation.pdf for a review of
expectile statistics and some thoughts on their interpretation.
Note: If you are interested in expectile-based distributional reinforcement learning, see issue #1 and this other repo.
This repopsitory provides an efficient implementation for computing the expectiles of a sample without resorting to generic iterative optimisation techniques.
See the expectile function in module expectiles.py,
the notebook ComputingExpectiles.ipynb
for a brief walkthough of the method,
and
derivation.pdf for a full derivation.
Made with 💜 by Matt.
[1] Dennis J Aigner, Takeshi Amemiya, and Dale J Poirier. On the estimation of production frontiers: maximum likelihood estimation of the parameters of a discontinuous density function. International Economic Review, pages 377–396, 1976.
[2] Whitney K Newey and James L Powell. Asymmetric least squares estimation and testing. Econometrica: Journal of the Econometric Society, pages 819–847, 1987.
[3] Linda Schulze Waltrup, Fabian Sobotka, Thomas Kneib, and Göran Kauermann. Expectile and quantile regression---david and goliath? Statistical Modelling, 15(5):433–456, 2015.