Quadratic estimation in mixed linear models with two variance components

Explicit expressions for Bayes invariant quadratic estimates, biased and unbiased, are presented and proved to cover the entire class of admissible estimates in the considered classes. An unbalanced genetic model is studied for demonstration.     

Nonlinear unbiased estimation in linear models †

In the paper the problem of nonlinear unbiased estimation of expectation in linear models is considered. The considerations are restricted to linear plus quadratic estimators with quadratic parts invariant under a group of translations. The one way classification model is considered in detail, for which an explicit formula for the locally best estimators is presented. A numerical evaluation of variances of the best estimators is given for some unbalanced one way classification models and compared with the variance of the ordinary linear estimators.     

Using Choquet integral in economics

This paper is devoted to application of the Choquet integral with respect to the monotone set functions in economics. We present the application in decision making, finance, insurance, social welfare and quality of life. The Choquet integral is used as the numerical representation of preference relation in decision making, as the “expected value” of future price in financial decision problems, as the insurance premium and as the social evaluation function. Received: March 2000; revised version: August 2001     

Individual control treatment in split-plot experiments

The paper deals with experiments laid out in a complete or an incomplete split-plot design in which one control (standard) treatment occurs in addition to the usual treatments. Usually the control (standard) treatment has been treated as one specific factor level. In this paper, in contrast to others in this area, the control (standard) may not be strictly connected with treatment combinations. The new incomplete split-plot designs with control satisfy all generally accepted methodological requirements, with special reference to the problems of randomisation. Moreover, tools are described which allow checking of the general balance or efficiency of the design, as well as performance of experiments with inference.     

The essentially complete class of rules in multinomial identification

The problem of identification within two groups is considered, when the space 𝔛 of the possible values of the observed random variable X is finite. Using an essentially complete class of tests hypothesis ξ=0 (ξis real) for the multivariate exponential family, an essentially complete class of sample-based identification rules has been found. Comparison of the rules to those derived from density estimators has shown that the latter constitute a subclass of the former.     

Influence of the gregarious instinct and individuals’ behavior patterns on macro migrations: Simulation experiments

The objective of the model is to simulate the migrations of social groups over certain geographical regions, influenced by the gregarious effect and individual behavior patterns. The people move in search of better work opportunities and welfare. The model components are regions and individuals belonging to certain social groups. A region is characterized by more than 30 parameters, such as geographical data, actual population statistics, education facilities, and work opportunities. For the social groups, the parameters include the demographic and educational statistics. The simulated individuals attempt to optimize their welfare by moving over the model map. Spontaneous migration, without apparent goal, is also considered. The region parameters change owing to the number and the parameters of incoming individuals, which provides a dynamic and nonlinear feedback. The qualitative results reveal that the model never reaches a steady state and that the social groups remain in periodical movement. The simulations are agent-based. No differential equations (like in the System Dynamics approach) or any extant theory or mathematical model is used.