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Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables

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  • Anastasiou, Andreas

Abstract

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a long established result. Explicit bounds for the distributional distance between the distribution of the MLE and the normal distribution have recently been obtained for the case of independent random variables. In this paper, a local dependence structure is introduced between the random variables and we give upper bounds which are specified for the Wasserstein metric.

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  • Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 171-181.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:171-181
    DOI: 10.1016/j.spl.2017.04.022
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    References listed on IDEAS

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    1. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
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    Cited by:

    1. Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m -dependent random variables," LSE Research Online Documents on Economics 83635, London School of Economics and Political Science, LSE Library.
    2. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    3. Steffen Betsch & Bruno Ebner, 2021. "Fixed point characterizations of continuous univariate probability distributions and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 31-59, February.

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