Abstract
The fundamental requirement in data analysis is the consistent estimation of a parameter. As the sample size increases, the precision of the estimator naturally improves, following a rate of \(n^{-1/2}\) for parameters under regular statistical models. However, when dealing with finite mixture models, it becomes evident that this rate is strongly influenced by how excessively the order of the mixture is specified. Chapter 8 sheds light on the development of the claimed best possible rate, which was \(n^{-1/4}\) when the order is over-specified. It is now widely recognized that the minimax rate is \(n^{-1/6}\) even when the order is merely over-specified by one. The overall scenario is considerably more intricate than initially expected, and this chapter is dedicated to deepening the understanding of the optimal rate of convergence and its implications under finite mixture models.
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Chen, J. (2023). Rate of Convergence. In: Statistical Inference Under Mixture Models. ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-99-6141-2_8
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DOI: https://doi.org/10.1007/978-981-99-6141-2_8
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