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The goal of this paper is associated with the study of global processes which change the world order and are accompanied with the aggravation of economic competition and geopolitical confrontation, which cause large-scale migration, radicalization of ethnicity and the rise of ethnic separatism. These processes contribute to the aggravation of interethnic antagonisms in multicultural countries and regions; therefore, it is necessary to search for adequate models of interethnic relations management in a multicultural society.

The methodological foundation of this research consists in activity, civilization, and transformation approaches, which allow understanding the specificity of global processes, the causes of the actualization of ethnic factor in the modern world and the search for new methods of interethnic relations management.

This paper presents an overview of models of interethnic relations management established in the western countries in the second half of the 20th century. The authors identify specific features of the assimilation and multiculturalism models for managing ethnic differences, their methods of regulation of interethnic relations in a multicultural environment. Their potential in solving the issues of adaptation of migrants and their integration in political and cultural space of the host society in the face of new global challenges and threats is assessed.

The authors of the paper justify the need for a new model of interethnic relations management which is able to forecast the global development trends and adequately respond to negative consequences of global processes.

For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.