Major Results of Research. · General-purpose computer systems of algorithms for the analysis and design of experiments that form the basis for the design of application program

· General-purpose computer systems of algorithms for the analysis and design of experiments that form the basis for the design of application program packages, dialogue systems, expert systems, etc. have been proposed, elaborated and investigated.

· Direct and dual-direct algorithms have been proposed, developed and investigated for building optimal (locally optimal) mini-max and bias experiment designs with linear and non-linear parameterization of the regression equation set for a compact domain of independent variable variation as well as algorithms for optimality criteria of convex functionals of information matrices.

· The task of the grouped response experiment analysis and design has been set and resolved.

· Methods of developing invariant and unbiased rules have been worked out for detection and identification of signals under a priori uncertainty on the basis of the approximation of distribution functions of the values under study.

· Methods of the signal parameter estimation under a priori uncertainty have been elaborated on the basis of the theory of effective estimation of distribution parameters by using complete sufficient statistics and the method of moments.

· New variational statements for solving nonlinear non-steady state problems of electromagnetism arising in complex technical devices have been developed as well as new approaches to solving 3D problems of electromagnetism.

· Distributions of statistics of non-parametric fitting criteria of the Kolmogorov, Smirnoff or Mises type in testing various complicated hypotheses by means of different estimation methods have been investigated. Approximations of statistics distribution laws of appropriate criteria for various complicated hypotheses have been built.

· A differential and geometric approach to constructing an asymptotic second-order nonlinear regression theory by the least square method has been developed.

Based on these investigations, general-purpose application program packages were elaborated for the experiment analysis and design on various computers; solutions to three-dimensional stationary and non-stationary problems of electromagnetism and heat transfer were proposed; software for automated measurement and control systems as well as an expert system to study multi-factor objects were elaborated. The teaching manual “Applied statistics. Rules for testing experimental and theoretical distribution agreement. Methodological recommendations” in two parts was written.

Дата добавления: 2015-07-18