Asymptotic analysis of parameter estimation for the Ewens--Pitman partition
| Autor: | Koriyama, Takuya, Matsuda, Takeru, Komaki, Fumiyasu |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We derive the exact asymptotic distribution of the maximum likelihood estimator $(\hat{\alpha}_n, \hat{\theta}_n)$ of $(\alpha, \theta)$ for the Ewens--Pitman partition in the regime of $0<\alpha<1$ and $\theta>-\alpha$: we show that $\hat{\alpha}_n$ is $n^{\alpha/2}$-consistent and converges to a variance mixture of normal distributions, i.e., $\hat{\alpha}_n$ is asymptotically mixed normal, while $\hat{\theta}_n$ is not consistent and converges to a transformation of the generalized Mittag-Leffler distribution. As an application, we derive a confidence interval of $\alpha$ and propose a hypothesis testing of sparsity for network data. In our proof, we define an empirical measure induced by the Ewens--Pitman partition and prove a suitable convergence of the measure in some test functions, aiming to derive asymptotic behavior of the log likelihood. Comment: 58 pages |
| Databáze: | arXiv |
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