Just when I thought I was starting to get my head around the multitudinous uses of convexity in statistics I was thrown by the following definition:
A function f over the interval (a,b) is convex if, for all choices of {x,y,z} satisfying a < x < y < z < b the [...]
I’ve been attempting to read an interesting NIPS 2007 paper entitled Estimating divergence functionals and the likelihood ratio by convex risk minimzation and realised my knowledge of convex analysis was sketchy at best.
Fortunately, Wikipedia pointed me to an excellent summary of the Legendre-Fenchel transformation by Hugo Touchette. A bit more digging around Hugo’s site led [...]