Curved exponential families

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.


Efron, Bradley. 1975. β€œDefining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency).” The Annals of Statistics 3 (6): 1189–1242.

β€”β€”β€”. 1978. β€œThe Geometry of Exponential Families.” The Annals of Statistics 6 (2): 362–76.

β€”β€”β€”. 2004. β€œThe Estimation of Prediction Error.” Journal of the American Statistical Association 99 (467): 619–32.

Keener, Robert W. 2009. β€œCurved Exponential Families.” In Theoretical Statistics, 85–99. Springer Texts in Statistics. Springer New York.