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Regularization with maximum entropy and quantum electrodynamics: the MERG(E) estimators

Macedo, Pedro; Scotto, Manuel; Silva, Elvira

Communications in Statistics - Simulation and Computation, 45 (2016), 1143-1157

It is well known that under fair conditions linear regression becomes a powerful statistical tool. In practice, however, some of these conditions are usually not satisfied and regression models become ill-posed, implying that the application of traditional estimation methods may lead to non-unique highly unstable solutions. Addressing this issue, in this article a new class of maximum entropy estimators suitable for dealing with ill-posed models, namely, for the estimation of regression models with small samples sizes affected by collinearity and outliers, is introduced. The performance of the new estimators is illustrated through several simulation studies.