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An asymptotic minimax risk bound for estimation of a linear functional relationship

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  • Nussbaum, M.

Abstract

We consider estimation of the parameter B in a multivariate linear functional relationship Xi=[xi]i+[xi]1i, Yi=B[xi]i+[xi]2i, i=1,...,n, where the errors ([zeta]1i', [zeta]2i') are independent standard normal and ([xi]i, i [set membership, variant] ) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n-1/2 is also established.

Suggested Citation

  • Nussbaum, M., 1984. "An asymptotic minimax risk bound for estimation of a linear functional relationship," Journal of Multivariate Analysis, Elsevier, vol. 14(3), pages 300-314, June.
    • Handle: RePEc:eee:jmvana:v:14:y:1984:i:3:p:300-314
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    Cited by:

    1. Kukush, Alexander & Maschke, Erich Otto, 2003. "The efficiency of adjusted least squares in the linear functional relationship," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 261-274, November.

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