Ryzhov A. An analysis of failure-time data by observations from mixture

The thesis is devoted to the problem of development of nonparametric methods for analysis of mixtures with varying concentrations by censored observations. An adaptive scheme was used to construct unbiased, uniformly consistent and asymptotically normal estimators of unknown CDFs of mixture's components. In what follows these adaptive estimators were used to produce test statistics when a problem of homogeneity of mixture's components is considered. Asymptotic properties of the proposed test statistics were studied. In case of two-component mixture a generalized least squares method is applied for constructing estimators of unknown concentrations of mixture's components. Two theorems establishing consistency and asymptotic normality of these estimators are formulated. Monte-Carlo simulations with fixed-size samples were performed to test theoretical results.