Asymptotics for minimisers of convex processes

Understand

By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions.

• This method is then applied to a fair range of different statistical estimation problems, including Cox regression, logistic and Poisson regression, least absolute deviation regression outside model conditions, and pseudo-likelihood estimation for Markov chains.
• Our paper has two aims.
• The first is to exposit the method itself, which in many cases, under reasonable regularity conditions, leads to new proofs that are simpler than the traditional proofs.