In the Empirical Estimating Equations (E^3) approach to estimation and inference estimating equations are replaced by their data-dependent empirical counterparts. It is odd but with E^3 there are models where the E^3-based estimator does not exist for some data set, and does exist for others....

Clinical data serve as a necessary basis for medical decisions. Consequently, the importance of methods that help officials quickly identify human tampering of data cannot be underestimated. In this paper, we suggest Benford’s Law as a basis for objectively identifying the presence of...

In 1881, Newcomb conjectured that the first significant digits (FSDs) of numbers in statistical tables would follow a logarithmic distribution with the digit “1†occurring most often. However, because Newcomb’s proposal was not presented with a theoretical basis, it was not...

Using a large deviations approach, Maximum A-Posteriori Probability (MAP) and Empirical Likelihood (EL) are shown to possess, under misspecification, an exclusive property of Bayesian consistency. Under conditions of consistency, regardless of prior the MAP estimator asymptotically coincides...

The Bayesian Sanov Theorem (BST) identifies, under both correct and incorrect specification of infinite dimensional model, the points of concentration of the posterior measure. Utilizing this insight in the context of Polya urn sampling, Bayesian nonparametric consistency is established. Polya...

Empirical Likelihood (EL) and other methods that operate within the Empirical Estimating Equations (E3) approach to estimation and inference are challenged by the Empty Set Problem (ESP). ESP concerns the possibility that a model set, which is data-dependent, may be empty for some data sets. To...