Abstract
The authors begin by reviewing the central pre-limit theorem, providing a careful definition and characterization of the limiting distributions. The authors develop a correct version of the theory of statistical estimation, and show its connection with the problem of the choice of an appropriate loss function.
A loss function should not be chosen arbitrarily. As they explain, the availability of certain mathematical conveniences (including the correctness of the formulation of the problem estimation) leads to rigid restrictions on the choice of the loss function.
The questions about the correctness of incorrectness of certain statistical problems may be resolved through appropriate choice of the loss function and/or metric on the space of random variables and their characteristics (including distribution functions, characteristic functions, and densities). Some auxiliary results from the theory of generalized functions are provided in an appendix.