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The efficiency of adjusted least squares in the linear functional relationship

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  • Kukush, Alexander
  • Maschke, Erich Otto

Abstract

A linear functional errors-in-variables model with unknown slope parameter and Gaussian errors is considered. The measurement error variance is supposed to be known, while the variance of errors in the equation is unknown. In this model a risk bound of asymptotic minimax type for arbitrary estimators is established. The bound lies above that one which was found previously in the case of both variances known. The bound is attained by an adjusted least-squares estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:261-274
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    References listed on IDEAS

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    1. Chi‐Lung Cheng & Hans Schneeweiss, 1998. "Polynomial regression with errors in the variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 189-199.
    2. 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.
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