Prediction under model uncertainty is an important and difficult issue. Traditional prediction methods (such as pretesting) are based on model selection followed by prediction in the selected model, but the reported prediction and the reported prediction variance ignore the uncertainty from the...

The well-known transformation theorem (or change-of-variables theorem) is difficult to prove, requiring knowledge of theorems in advanced analysis. For this reason, it is stated without proof in all the statistics textbooks we know of. Here, we provide a new and much simpler proof, by exploiting...

Sensitivity analysis is important for its own sake and also in combination with diagnostic testing. We consider the question how to use sensitivity statistics in practice, in particular how to judge whether sensitivity is large or small. For this purpose we distinguish between absolute and...

Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these...

Empirical growth research faces a high degree of model uncertainty. Apart from the neoclassical growth model, many new (endogenous) growth models have been proposed. This causes a lack of robustness of the parameter estimates and makes the determination of the key determinants of growth...

In this paper we shall be interested in two questions on extremes relating to world records in athletics. The first question is: what is the ultimate world record in a specific athletics event (such as the 100m for men or the high jump for women), given today's state of the art? Our second...

Overconfidence seems to be an essential aspect of human nature, and one way to study overconfidence is to consider students' forecasts of their exam grades. Part of a student's grade expectation is based on the student's previous academic achievements; what remains can be interpreted as...

The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model averaging estimators when accounting for problems of...

Bayesian model averaging attempts to combine parameter estimation and model uncertainty in one coherent framework. The choice of prior is then critical. Within an explicit framework of ignorance we define a ‘suitable' prior as one which leads to a continuous and suitable analog to the pretest...

This papers offers a theoretical explanation for the stylized fact that forecast combinations with estimated optimal weights often perform poorly in applications. The properties of the forecast combination are typically derived under the assumption that the weights are fixed, while in practice...