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A note on constrained estimation in the simple linear measurement error model

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  • Davidov, Ori
  • Griskin, Vladimir

Abstract

It is well known that for any sample size the estimator for the slope in the simple linear measurement error model does not possess even a first moment. Addressing this issue constrained maximum likelihood estimators (MLEs) are developed using three different approaches, under a number of identifiability assumptions. The constrained MLEs have finite moments of all orders. They are asymptotically equivalent to the MLE, which is known to be consistent and asymptotically normal. Numerical investigation shows that the constrained MLEs perform well under a wide variety of experimental settings.

Suggested Citation

  • Davidov, Ori & Griskin, Vladimir, 2008. "A note on constrained estimation in the simple linear measurement error model," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 508-517, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:508-517
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    References listed on IDEAS

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    1. Khuri A. & Casella G., 2002. "The Existence of the First Negative Moment Revisited," The American Statistician, American Statistical Association, vol. 56, pages 44-47, February.
    2. Chi‐Lun Cheng & Hans Schneeweiss & Markus Thamerus, 2000. "A small sample estimator for a polynomial regression with errors in the variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 699-709.
    3. Davidov, Ori, 2005. "Estimating the slope in measurement error models--a different perspective," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 215-223, March.
    4. Wenjiang J. Fu, 2003. "Penalized Estimating Equations," Biometrics, The International Biometric Society, vol. 59(1), pages 126-132, March.
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