The efficiency of adjusted least squares in the linear functional relationship

  • Authors:

  • Alexander Kukush;Erich Otto Maschke

  • Affiliations:

  • National Taras Shevchenko, University of Kiev, Vladimirskaya st. 64, 01033 Kiev, Ukraine and Ludwig-Maximilian-University, Akademiestr. 1, 80799 Munich, Germany;Ludwig-Maximilian-University, Akademiestr. 1, 80799 Munich, Germany

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2003

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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.