We consider the question whether top tennis players in a top tournament (Wimbledon) employ an optimal (efficient) service strategy. We show that top players do not, in general, follow an optimal strategy, and we provide a lower bound of the inefficiency. The inefficiency regarding winning a...

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...

We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parametrization of rotation matrices governing...

A linear structure is a family of matrices that satisfy a given set of linear restrictions, such as symmetry or diagonality. We add to the literature on linear structures by studying the family of matrices where all diagonal elements are zero, and discuss two econometric examples where these...

A Bayesian typically uses data and a prior to produce a posterior. In practice, the data and the posterior are often observed but not the prior. We shall follow the opposite route, using data and the posterior information to reveal the prior. We then apply this theory to (equilibrium) climate...

We consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its...

An explanation of the Dunning-Kruger effect is provided which does not require any psychological explanation, because it is derived as a statistical artefact. This is achieved by specifying a simple statistical model which explicitly takes the (random) boundary constraints into account. This...

Gauss' 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss' arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive...

Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and try to understand why...

We extend the results of De Luca et al. (2021) to inference for linear regression models based on weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor. We concentrate on inference about a single focus parameter, interpreted as the causal effect of...