Titlebook: Statistical Inference Under Mixture Models; Jiahua Chen Book 2023 Springer Nature Singapore Pte Ltd. 2023 EM-algorithm.EM-test.Hypothesis

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-Test for Homogeneity,using EM-iterations from the best-fitted null model in a specific manner. This chapter introduces the concept and the conclusions related to the simple homogeneity case, with the more complex scenarios addressed in the subsequent chapter. It unveils the somewhat more intricate technical advantages of this approach.

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Estimation Under Finite Normal Mixture Models,characteristics. Notably, the general finite normal mixture model boasts an unbounded likelihood function, rendering the straightforward maximum likelihood estimator of the mixing distribution inconsistent. However, in the case of the univariate normal mixture with a structured scale parameter, the

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Consistent Estimation Under Finite Gamma Mixture,thin this framework is unbounded, theoretically leading to an inconsistent maximum likelihood estimator. However, it is worth noting that, in practice, this inconsistency rarely manifests in data analysis. Nevertheless, this chapter provides an in-depth exploration of the development of a consistent

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Geometric Properties of Non-parametric MLE and Numerical Solutions,enge arises from the infinite dimension of the nonparametric space, making the resulting optimization problem seem insurmountable. However, the nonparametric maximum likelihood estimator is known to have finite support, meaning it assigns positive probabilities to a finite set of mixing parameter va

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