Minimax Estimation in Regression under Sample Conformity Constraints

The paper is devoted to the guaranteeing estimation of parameters in uncertain stochastic nonlinear regression. loss function conditional mean square error given available observations. distribution regression partially unknown, and uncertainty described by a subset probability distributions with known compact domain. essential feature usage some additional constraints describing conformity realized observation sample. contains various examples indices. task formulated as minimax optimization problem, which, turn, solved terms saddle points. presents characterization both optimal estimator set least favorable distributions. points are found via solution dual finite-dimensional which simpler than initial problem. proposes numerical mesh procedure interconnection between under constraint, their Pareto efficiency sense vector criterion also indicated. influence on performance demonstrated illustrative examples.