We are quite pleased to learn that our paper on "frequentist model averaging" is highly cited. Part of the reason is that it hopefully is seen as having broad relevance, dealing with issues that concern not only specialists but actually mainstream statistics, both theoretical and applied. The paper deals with an issue that has been if not ignored, then "left aside" for much of the history of statistical model fitting: How does the selection of a model influence further inference? We are glad that other people are taking up this issue as well, and are now beginning to use more appropriate methods, as opposed to the still-common practice that ignores the model selection step in data analyses, leading to underreporting variability and over-optimism about confidence intervals and testing results, which we quantify in our paper.

Our paper provides a framework for studying the effects of statistical model selection and more generally of model averaging strategies. We are the first to give accurate descriptions of distributions and risk functions of estimators after model selection and of estimators averaged across models. Our framework effectively handles the aspect of modelling bias—that most models do not quite match the complex reality. The results we reach are rather general in nature, and facilitate comparison of different selection methods. Our research has also led to completely new model selection methods, e.g., the "Focused Information Criterion" (see Claeskens and Hjort, Journal of the American Statistical Association, 98: 900-916, 2003).

"All models are wrong, but some are useful." - George E.P. Box

Thus there is a need for constructing statistical model selection methods, and some have been around for at least 30 years. Typical data analysis, from simple regressions to highly complex phenomena, therefore take the form of: (1) select a model, (2) give conclusions in terms of confidence intervals, p-values, etc. The trouble has been that stage (2) really ought to take stage (1) into account, but statistical practice has been to proceed with (2) as if the selected model had been chosen in advance. That this is not good enough should be made clear from the fact that when an experiment is run a second time, a data set is generated that might be only slightly different from the first, but easily leads to selecting a different final model. Our approach deals with this uncertainty and gives a precise description of, for example, the distribution of estimators obtained by using a statistically selected model. When using these results, correct conclusions of the data analysis can be stated, without being overly optimistic regarding, e.g., confidence intervals and p-values (as has been the common practice).

We have collaborated on various projects since we first met at the Australian National University in 2000, where we had been invited by Professor Peter Hall, independently of each other. One of our papers was concerned with testing the fit of a given parametric model, where we used model selection criteria in the construction of the test. This led to considerations of "how does a test perform inside a randomly selected model?" Obviously, its distribution is influenced by not knowing in advance which model gets selected. To our surprise no such equivalent theory existed for estimators in general models. In the literature some authors already pointed out the problem several years ago, but no satisfactory solution had been provided. We then decided to take the challenge and tackle this long standing problem.