Curved exponential families

April 19, 2016 — April 19, 2016

Curved exponential families generalise exponential families while preserving some of the magic, I guess?

Credited to (Efron 2004) and used in Efron (1978) to show some nice behaviour for degrees of freedom-based penalties. Will read soon.


1 References

Efron. 1975. Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency).” The Annals of Statistics.
———. 1978. The Geometry of Exponential Families.” The Annals of Statistics.
———. 2004. The Estimation of Prediction Error.” Journal of the American Statistical Association.
Keener. 2009. Curved Exponential Families.” In Theoretical Statistics. Springer Texts in Statistics.