Models are considered in which lsquotruersquo lifetimes are generated by a Weibull regression model and measured lifetimes are determined from the true times by certain measurement error models. Adjusted estimators are obtained under one parametric specification. The bias properties of these estimators and standard estimators are compared both theoretically, using small measurement error asymptotics, and by simulation. The standard estimators of regression coefficients, other than the intercept, are bias-robust. The adjusted estimator of the shape parameter removes the bias of the standard estimator
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