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...

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...

Methods, like Maximum Empirical Likelihood (MEL), that operate within the Empirical Estimating Equations (E3) approach to estimation and inference are challenged by the Empty Set Problem (ESP). We propose to return from E3 back to the Estimating Equations, and to use the Maximum Likelihood...

Criterion choice is such a hard problem in information recovery and in estimation and inference. In the case of inverse problems with noise, can probabilistic laws provide a basis for empirical estimator choice? That is the problem we investigate in this paper. Large Deviations Theory is used to...