# Curved exponential families

April 19, 2016 — April 19, 2016

geometry

probability

statistics

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.

Examples?

## 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.