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Asymptotic properties of maximum likelihood estimators for a generalized Pareto-type distribution

机译：广义帕累托型分布的最大似然估计的渐近性质

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摘要

Astola and Danielian [1], using stochastic birth-death process, have proposed a regular four-parameter discrete probability distribution, called generalized Pareto-type model, which is an appealing distribution for modeling phenomena in Bioinformatics. Farbod and Gasparian [5], fitted this distribution to the two sets of real data, and have derived conditions under which a solution for the system of likelihood equations exists and coincides with the maximum likelihood estimators (MLE) for the model unknown parameters. Also, in [5], an accumulation method for approximate computation of the MLE has been considered with simulation studies. In this paper we show that for sufficiently large sample size the system of likelihood equations has a solution, which according to [5], coincides with the MLE of vector-valued parameter for the underlying model. Besides, we establish asymptotic unbiasedness, weak consistency, asymptotic normality, asymptotic efficiency, and convergence of arbitrary moments of the MLE, by verifying the so-called regularity-conditions.
机译：Astola和Danielian [1]使用随机的出生-死亡过程，提出了一个规则的四参数离散概率分布，称为广义帕累托型模型，这是一种用于在生物信息学中建模现象的吸引人的分布。 Farbod和Gasparian [5]将这种分布拟合到两组真实数据中，并推导了条件，在该条件下，存在似然方程组的解，并且与模型未知参数的最大似然估计器（MLE）一致。同样，在[5]中，已经通过模拟研究考虑了用于MLE近似计算的累积方法。在本文中，我们表明对于足够大的样本量，似然方程组具有一个解，根据[5]，该解与底层模型的矢量值参数的MLE相符。此外，通过验证所谓的正则条件，我们建立了渐近无偏性，弱一致性，渐近正态性，渐近效率和MLE任意时刻的收敛性。

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