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On asymptotics of the distributions of some two-step statistical estimators of a mutlidimensional parameter

Abstract

We study the accuracy of estimation of unknown parameters in the case of two-step statistical estimates admitting special representations. An approach to the study of such problems previously proposed by the authors is extended to the case of the estimation of a multidimensional parameter. As a result, we obtain necessary and sufficient conditions for the weak convergence of the normalized estimation error to a multidimensional normal distribution.

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Correspondence to Yu. Yu. Linke.

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Original Russian Text © Yu. Yu. Linke and A. I. Sakhanenko, 2013, published in Matematicheskie Trudy, 2013, Vol. 16, No. 1, pp. 89–120.

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Linke, Y.Y., Sakhanenko, A.I. On asymptotics of the distributions of some two-step statistical estimators of a mutlidimensional parameter. Sib. Adv. Math. 24, 119–139 (2014). https://doi.org/10.3103/S1055134414020035

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Keywords

  • asymptotically normal estimator
  • improvement of statistical estimates
  • two-step estimator
  • multidimensional parameter
  • regression