UPenn STAT928 notes

"In this paper we develop a new class of double generalized linear models, introducing a random effect component in the link function describing the linear predictor related to the precision parameter. This is a useful procedure to take into account extra variability and also to make the model more robust. The Bayesian paradigm is adopted to make inference in this class of models. Samples of the joint posterior distribution are draw using standard MCMC procedures. Finally, we illustrate this algorithm by considering simulated and real data sets."

"Generalized linear models have become a. standard class of models for data analysts. However in some applications, heterogeneity in samples is too great to be explained by the simple variance function implicit in such models. Utilizing a. two parameter exponential family which is overdispersed relative to a specified one parameter exponential family enables the creation of classes of overdispersed generalized linear models (OGLM’s) which are analytically attractive."

R.A Fisher's classical paper outlining the maximum likelihood principle and the notions of sufficiency, efficiency and consistency.

"If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically distributed data. We do not need the law of large numbers (LLN) or the central limit theorem (CLT). We do not need sample size going to infinity or anything going to infinity.

The theory presented here is a combination of Le Cam style involving local asymptotic normality (LAN) and local asymptotic mixed normality (LAMN) and Cramér style involving derivatives and Fisher information. The main tool is convergence in law of the log likelihood function and its derivatives considered as random elements of a Polish space of continuous functions with the metric of uniform convergence on compact sets. We obtain results for both one-step-Newton estimators and Newton-iterated-to-convergence estimators."

What to do when "experiments" can not be controlled (not much, but indoctrination helps) - predates current IV methodology?

"This paper discusses some subtle, and largely overlooked, differences between conceptual and mathematical optimization goals in statistics, and illustrates them by examples."

Additive regression models from 1924, together with an algorithm which looks even more labour intensive than Whittaker graduation!

Whittaker introduces 1D smoothing in 1922, complete with the Bayesian derivation. There is an earlier German paper with a similar model.