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An application of approximate finite sample results to parameter estimation in a linear errors‐in‐variables model

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  • R. Friedmann
  • H. J. Mittag
  • A. Brandtstater

Abstract

In the simple errors‐in‐variables model the least squares estimator of the slope coefficient is known to be biased towards zero for finite sample size as well as asymptotically. In this paper we suggest a new corrected least squares estimator, where the bias correction is based on approximating the finite sample bias by a lower bound. This estimator is computationally very simple. It is compared with previously proposed corrected least squares estimators, where the correction aims at removing the asymptotic bias or the exact finite sample bias. For each type of corrected least squares estimators we consider the theoretical form, which depends on an unknown parameter, as well as various feasible forms. An analytical comparison of the theoretical estimators is complemented by a Monte Carlo study evaluating the performance of the feasible estimators. The new estimator proposed in this paper proves to be superior with respect to the mean squared error.

Suggested Citation

  • R. Friedmann & H. J. Mittag & A. Brandtstater, 1991. "An application of approximate finite sample results to parameter estimation in a linear errors‐in‐variables model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(2), pages 93-106, June.
    • Handle: RePEc:bla:stanee:v:45:y:1991:i:2:p:93-106
    DOI: 10.1111/j.1467-9574.1991.tb01297.x
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    Cited by:

    1. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.

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