A method for estimating the power of moments

Let X be an observable random variable with unknown distribution function [Formula: see text] , [Formula: see text] , and let [Formula: see text] We call θ the power of moments of the random variable X. Let [Formula: see text] be a random sample of size n drawn from [Formula: see text] . In this pap...

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Detalles Bibliográficos
Autores principales: Chang, Shuhua, Li, Deli, Qi, Yongcheng, Rosalsky, Andrew
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5840234/
https://www.ncbi.nlm.nih.gov/pubmed/29540973
http://dx.doi.org/10.1186/s13660-018-1645-7
Descripción
Sumario:Let X be an observable random variable with unknown distribution function [Formula: see text] , [Formula: see text] , and let [Formula: see text] We call θ the power of moments of the random variable X. Let [Formula: see text] be a random sample of size n drawn from [Formula: see text] . In this paper we propose the following simple point estimator of θ and investigate its asymptotic properties: [Formula: see text] where [Formula: see text] , [Formula: see text] . In particular, we show that [Formula: see text] This means that, under very reasonable conditions on [Formula: see text] , [Formula: see text] is actually a consistent estimator of θ.

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