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A sequence of estimators \(W_n = W_n(\boldsymbol {X})\) is consistent for the parameter \(\theta \) if, \(\forall \varepsilon >0\) and \(\forall \theta \in \Theta \) , it holds: \(\displaystyle \lim _{n\to +\infty } \mathbb {P}_{\theta }\left (|W_n -\theta | <\varepsilon \right )=1; \) that is \(W_n \overset {p}{\to }\theta \) .

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Asymptotic Statistics

  • 章节

  • 发表日期：

    2025年

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  • Francesca Gasperoni,
  • Francesca Ieva,
  • Anna Maria Paganoni

摘要

A sequence of estimators \(W_n = W_n(\boldsymbol {X})\) is consistent for the parameter \(\theta \) if, \(\forall \varepsilon >0\) and \(\forall \theta \in \Theta \) , it holds: \(\displaystyle \lim _{n\to +\infty } \mathbb {P}_{\theta }\left (|W_n -\theta | <\varepsilon \right )=1; \) that is \(W_n \overset {p}{\to }\theta \) .