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.
