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A goodness-of-fit test for a polynomial errors-in-variables model

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Ukrainian Mathematical Journal Aims and scope

Abstract

Polynomial regression models with errors in variables are considered. A goodness-of-fit test is constructed, which is based on an adjusted least-squares estimator and modifies the test introduced by Zhu et al. for a linear structural model with normal distributions. In the present paper, the distributions of errors are not necessarily normal. The proposed test is based on residuals, and it is asymptotically chi-squared under null hypothesis. We discuss the power of the test and the choice of an exponent in the exponential weight function involved in test statistics.

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REFERENCES

  1. C.-L. Cheng H. Schneeweiss (1998) ArticleTitlePolynomial regression with errors in the variables J. R. Statist. Soc. B 60 189–199

    Google Scholar 

  2. R. J. Carroll D. Ruppert L. A. Stefanski (1995) Measurement Error in Nonlinear Models Chapman and Hall London

    Google Scholar 

  3. C.-L. Cheng H. Schneeweiss M. Thamerus (2000) ArticleTitleA small sample estimator for a polynomial regression with errors in the variables J. R. Statist. Soc. B 62 699–709

    Google Scholar 

  4. C.-L. Cheng H. Schneeweiss (2002) On the polynomial measurement error model S. Huffel Particlevan P. Lemmerling (Eds) Total Least Squares and Errors-in-Variables Modeling Kluwer Dordrecht 131–143

    Google Scholar 

  5. L. Zhu, H. Cui, and K. W. Ng, “Testing lack-of-fit for linear errors-in-variables model,” Acta Appl.Math. (to appear).

  6. H. P. Rosenthal (1970) ArticleTitleOn the subspaces of L p (p > 2) spanned by sequences of independent random variables Isr. J. Math. 8 273–303

    Google Scholar 

  7. H. Schneeweiss T. Nittner (2000) Estimating a Polynomial Regression with Measurement Errors in the Structural and in the Functional Case-a Comparison SeriesTitleDiscuss. Paper NumberInSeries197 Sonderforschungbereich 386, Univ. Munich Munich

    Google Scholar 

  8. A. Kukush and H. Schneeweiss, “A comparison of asymptotic covariance matrices of adjusted least squares and structural least squares in error ridden polynomial regression,” J.Statist.Plan.Inference (to appear).

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Authors and Affiliations

  1. Academia Sinica, Taipei, Republic of China

    C.-L. Cheng

  2. Shevchenko Kiev University, Kiev

    A. G. Kukush

Authors
  1. C.-L. Cheng
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  2. A. G. Kukush
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 527–543, April, 2004.

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Cheng, CL., Kukush, A.G. A goodness-of-fit test for a polynomial errors-in-variables model. Ukr Math J 56, 641–661 (2004). https://doi.org/10.1007/s11253-005-0009-x

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  • DOI: https://doi.org/10.1007/s11253-005-0009-x

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