The Living Thing / Notebooks : Curved exponential families

Curved exponential families generalise exponential families and preserve some of the magic, I guess? I suspect they arise in generalised linear models ndpossibly more general places.

Credited to Efro75 and used in Efro04 to show some nice behaviour for degrees of freedom-based penalties. Will read soon.

Refs

Efro75
Efron, B. (1975) Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency). The Annals of Statistics, 3(6), 1189–1242. DOI.
Efro78
Efron, B. (1978) The Geometry of Exponential Families. The Annals of Statistics, 6(2), 362–376. DOI.
Efro04
Efron, B. (2004) The Estimation of Prediction Error. Journal of the American Statistical Association, 99(467), 619–632. DOI.
Keen09
Keener, R. W.(2009) Curved Exponential Families. In Theoretical Statistics (pp. 85–99). Springer New York