A Note on Estimation of Log-Linear Model with Measurement Errors and Without Extra Information

10.29973/JCSA.200509.0006

Steve Y. H. Huang；Xaero Y. H. Lin

Errors-in-variables ； measurment error ； log-linear ； Poisson regression

中國統計學報

43卷3期（2005 / 09 / 01）

353 - 369

英文

In the analysis of measurement error models, the naive estimators arc inconsistent and biased. For consistent estimation, one usually needs extra information such as additional observed variables or known parameters. A common assumption about extra information is the knowledge of measurement errors' variances. However, such variances arc usually ”known” by estimates computed from replicate measurements or some external sources. In practice, it may happen that replicates arc hard to obtain or some extra information may not be available. Both can cause problems in knowing the variances, and flaw any estimation method based on such information. In the present paper, we develop an estimation method for the log-linear model with measurement errors and without extra informations. Furthermore, this method doesn't require any distribution assumption on the measurement error ridden covariate. It is applicable when the measurement error ridden covariate is treated as fixed but unknown constant. Briefly, a functional measurement error model can be analyzed without extra information, which is an uncommon phenomenon in error-in-variables models.

1. Amemiya, Y.,Fuller, W.A.(1988).Estimation for the Nonlinear Functional Relationship.Annals of Statistics,16,147-160.
2. Carroll, R. J.,Ruppert, D.,Stefanski, L. A.(1995).Measurement Error in Nonlinear Models.London:Chapman and Hall.
3. Cheng, C. L.,Van Ness, J. W.(1999).Statistical Regression with Measurement Error.London: Arnold and New York:Oxford University Press.
4. Fuller, W.A.(1987).Measurement Error Models.New York:John Wiley and Sons.
5. Guo, J. Q.,Li, T.(2002).Poisson regression models with errors-in-variables: implicatin and treatment.Journal of Statistical Planning and Inference,104,391-401.
6. Nakamura, T.(1990).Corrected Scores Function for Errors-in-Variables Models: Methodology and Application to Generalized Linear Models.Biometrika,77,127-137.