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\footnotesize
\noindent Statistica Sinica {\bf 15}(2005), 1049-1068

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\centerline{\large\bf TESTING THE ADEQUACY FOR A GENERAL }
\vspace{2pt}
\centerline{\large\bf LINEAR ERRORS-IN-VARIABLES MODEL}
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\author{Lixing Zhu and  Hengjian Cui}
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\centerline{\it The University of Hong Kong and Beijing Normal University}
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\begin{quotation}
\noindent {\it Abstract:}
In testing the adequacy of a regression model, the conditional expectation of the residuals
 given the observed covariate is often employed to  construct lack-of-fit tests. However,
 in the errors-in-variables model, the resiudal  is  biased and cannot be used directly. In this paper,
  by correcting for the bias, we suggest   lack-of-fit tests of score type for a general linear
  errors-in-variables model. The polynomial model is a special case.   The tests are asymptotically
chi-squared under the null hypothesis. The choice of scores
involved in the test statistics  and  the power properties are
investigated. A simulation study shows that the tests perform
well. Application to two data sets is also made. The approach can
readily be extended to handle general parametric models.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Bias correction,  errors-in-variables model, lack-of-fit test.\par
\end{quotation}

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