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A review of asymptotic theory of estimating functions

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Abstract

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic distribution are treated separately. Our conditions are not minimal, but can be verified for many interesting stochastic process models. Several examples illustrate the wide applicability of the theory and why the generality is needed.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu and CNRS UMR 7586, Université P. et M. Curie (Paris-6), 75252, Paris Cédex 05, France

    Jean Jacod

  2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark

    Michael Sørensen

Authors
  1. Jean Jacod
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  2. Michael Sørensen
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Correspondence to Michael Sørensen.

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Jacod, J., Sørensen, M. A review of asymptotic theory of estimating functions. Stat Inference Stoch Process 21, 415–434 (2018). https://doi.org/10.1007/s11203-018-9178-8

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  • DOI: https://doi.org/10.1007/s11203-018-9178-8

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