Nonlinear Estimation of Parameters in a Statistically Uncertain Model

Abstract

A problem of esimation of parameters in a statistically uncertain model is discussed. A generalized case is investigated when the measurement error has both a random component with the normal distribution and a statistically uncertain component that obeys only a geometric constraint. An approach to estimation of the set of the most probable states and to analysis of the sample consistency is suggested. Algorithms for direct construction of informational sets are used both for estimation of the admissible values of parameters and for analysis of consistency of the sample.