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The monograph is devoted to the study of asymptotic properties of statistical plausibility relations in various models of incomplete observations and to the use of these properties in the tasks of the theory of evaluation and verification of statistical hypotheses. The models of incomplete observations as a whole are obtained by random censoring on the right and on both sides of the random values of interest in the models of competing risks. The main results of the monograph are the establishment of asymptotic representations for the statistics of plausibility ratio in the models of incomplete observations, which follow the properties of local asymptotic normality for the statistics of plausibility ratio, as well as their use in the theory of evaluation and verification of hypotheses. In contrast to the classical results of Hayek and Le Kam in case of complete observations, the monograph uses methods of strong approximation and martingals.This book has been translated with Artificial Intelligence.