A symmetric version of the Neyman-Pearson test is developed for discriminating between sets of hypotheses and is extended to encompass a new formulation of the problem of parameter estimation based on finite data sets. Such problems can arise in distributed sensing and localization problems in sensor networks, where sensor data must be compressed to account for communication constraints. In thi...

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating functions are found, and the corresponding estimators are shown to be consistent and asymptotically normal. The discussion covers GMM, quasi-l...