On weak structural sufficiency

Abstract

In this paper, we consider sufficiency of the pair \((t,\pi )\) where \(\pi \) is a canonical projection which is maximal invariant and t is a maximum likelihood estimator which is weakly equivariant. We define weak structural sufficiency for \((t,\pi )\) and then we will consider the conditions under which \((t,\pi )\) is weakly structurally sufficient and investigate its properties. For the case in which the group on the parameter space is transitive, and the stabilizer group is characteristic and also for trivial-transitive spaces obtain new results on weak structural sufficiency.

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Correspondence to Mehdi Shams.

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Shams, M. On weak structural sufficiency. Bol. Soc. Mat. Mex. 26, 1313–1332 (2020). https://doi.org/10.1007/s40590-019-00259-x

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Keywords

  • Topological group
  • Characteristic subgroup
  • Invariance
  • Weak equivariance
  • Weak structural sufficiency
  • Maximum likelihood estimator
  • Trivial-transitive space

Mathematics Subject Classification

  • 62F10
  • 54H11