Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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An Alternative Proof of the Asymptotic Behavior of GLSE in Polynomial MEM

  • Myung-Sang Moon (Assistant Professor, Department of Statistics, Yonsei University, Wonju-City, Kangwon-Do, 222-701, Korea)
  • Published : 1996.12.01
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Abstract

Polynomial measurement error model(MEM) with one predictor is considered. It is briefly mentioned that Chan and Mak's generalized least squares estimator(GLSE) can be derived more easily if Hermite polynomial concept is applied. It is proved that GLSE derived using new procedure is equivalent to the estimator obtained from corrected score function. Finally, much simpler proof of the asymptotic behavior of GLSE than that of Chan and Mak is provided. Much simpler formula of asymptotic covariance matrix of GLSE is a part of that proof.

Keywords

References

  1. Journal of the Royal Statistical Society, Series B v.47 On the Polynomial Functional Relationship Chan, L. K.;Mak, T. K.
  2. Measurement Error Models Fuller, W. A.
  3. Computaitonal Statistics & Data Analysis v.19 Polynomial Measurement Error Modeling Moon, M. S.;Gunst, R. F.
  4. Biometrika v.77 Corrected Score Function for Errors-in variables Models: Methodology and Application to Generalized Linear Models Nakamura, T.
  5. Communication in Statistics-Theory and Methods v.18 Unbiased Estimation of a Nonlinear Function of a Normal Mean with Application to Measurement Error Models Stefanski, L.