论文标题
EWENS分区的最大似然估计器的渐近混合正态性
Asymptotic mixed normality of maximum likelihood estimator for Ewens--Pitman partition
论文作者
论文摘要
本文研究了Ewens的参数估计的渐近性能 - 参数$ 0 <α<1 $和$θ>-α$。特别是，我们表明，$α$的最大似然估计器（MLE）为$ n^{α/2} $ - 一致，并收敛于正常分布的方差混合物，其中方差受mittag-leffler分布的控制。此外，我们表明涉及随机统计量的适当归一化消除了方差的随机性。在此结果的基础上，我们为$α$构建了一个近似置信区间。我们的证明依赖于稳定的Martingale Central Limit定理，该定理具有独立感兴趣。
This paper investigates the asymptotic properties of parameter estimation for the Ewens--Pitman partition with parameters $0<α<1$ and $θ>-α$. Especially, we show that the maximum likelihood estimator (MLE) of $α$ is $n^{α/2}$-consistent and converges to a variance mixture of normal distributions, where the variance is governed by the Mittag-Leffler distribution. Moreover, we show that a proper normalization involving a random statistic eliminates the randomness in the variance. Building on this result, we construct an approximate confidence interval for $α$. Our proof relies on a stable martingale central limit theorem, which is of independent interest.
