Second-order asymptotic minimax estimation in the presence of a nuisance parameter

Z. M. Landsman; B. Ya Levit

Second-order asymptotic minimax estimation in the presence of a nuisance parameter

Department of Statistics

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Abstract

We consider second-order minimax estimation of the structural parameter θ₁ in the presence of a nuisance parameter θ₂ as the number of observations n → ∞. We show that the effect of the nuisance parameter is largely determined by a 'nontraditional' object in mathematical statistics - vector field X = ∂/∂θ₁ + J₁₂/J₁₁∂/∂θ₂, where J₁₁ and J₁₂ are elements of the inverse Fisher information matrix. As part of this study, second-order Bayesian estimators of the structural parameter in the presence of a nuisance parameter and asymptotic expansions of their risk functions are derived, and the ″ ″ is investigated.

Original language	English
Pages (from-to)	226-244
Number of pages	19
Journal	Problems of Information Transmission
Volume	26
Issue number	3
State	Published - Jan 1991

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Computer Networks and Communications

Cite this

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AB - We consider second-order minimax estimation of the structural parameter θ1 in the presence of a nuisance parameter θ2 as the number of observations n → ∞. We show that the effect of the nuisance parameter is largely determined by a 'nontraditional' object in mathematical statistics - vector field X = ∂/∂θ1 + J12/J11∂/∂θ2, where J11 and J12 are elements of the inverse Fisher information matrix. As part of this study, second-order Bayesian estimators of the structural parameter in the presence of a nuisance parameter and asymptotic expansions of their risk functions are derived, and the ″ ″ is investigated.

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Second-order asymptotic minimax estimation in the presence of a nuisance parameter

Abstract

ASJC Scopus subject areas

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