Ioannis Kosmidis

A generic algorithm for reducing bias in parametric estimation

A general iterative algorithm is developed for the computation of reduced-bias parameter estimates in regular statistical models through adjustments to the score function. The algorithm unifies and provides appealing new interpretation for iterative methods that have been published previously for some specific model classes. The new algorithm can usefully be viewed as a series of iterative bias corrections, thus facilitating the adjusted score approach to bias reduction in any model for which the first- order bias of the maximum likelihood estimator has already been derived. The method is tested by application to a logit-linear multiple regression model with beta-distributed responses; the results confirm the effectiveness of the new algorithm, and also reveal some important errors in the existing literature on beta regression.

Simulating events of unknown probabilities via reverse time martingales

Let s∈(0,1) be uniquely determined but only its approximations can be obtained with a finite computational effort. Assume one aims to simulate an event of probability s. Such settings are often encountered in statistical simulations. We consider two specific examples. First, the exact simulation of non-linear diffusions ([3]). Second, the celebrated Bernoulli factory problem ([10, 13]) of generating an f(p)-coin given a sequence X1,X2,… of independent tosses of a p-coin (with known f and unknown p). We describe a general framework and provide algorithms where this kind of problems can be fitted and solved. The algorithms are straightforward to implement and thus allow for effective simulation of desired events of probability s. Our methodology links the simulation problem to existence and construction of unbiased estimators.

Modeling outcomes of soccer matches

We compare various extensions of the Bradley–Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley–Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley–Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.

Median bias reduction in random-effects meta-analysis and meta-regression

The reduction of the mean or median bias of the maximum likelihood estimator in regular parametric models can be achieved through the additive adjustment of the score equations. In this paper, we derive the adjusted score equations for median bias reduction in random-effects meta-analysis and meta-regression models and derive efficient estimation algorithms. The median bias-reducing adjusted score functions are found to be the derivatives of a penalised likelihood. The penalised likelihood is used to form a penalised likelihood ratio statistic which has known limiting distribution and can be used for carrying out hypothesis tests or for constructing confidence intervals for either the fixed-effect parameters or the variance component. Simulation studies and real data applications are used to assess the performance of estimation and inference based on the median bias-reducing penalised likelihood and compare it to recently proposed alternatives. The results provide evidence on the effectiveness of median bias reduction in improving estimation and likelihood-based inference.

Correction to: Modeling outcomes of soccer matches

The Publisher regrets an error in the presentation of Table 5.