Abstract:
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In this talk, I will consider semiparametric mixture models where the population consists of two or more homogeneous groups with different location parameters. In this case, if one leaves the component density completely unspecified, the estimation may fail due to the lack of identifiability. Instead, researchers often restricted the component density to be symmetric so that the model becomess identifiable. I will introduce several existing methods to estimate the density, and propose the doubly smoothed maximum likelihood estimator which can effectively eliminate potential biases while maintaining a high efficiency. Some numerical examples are also presented to demonstrate the performance of the proposed method.
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