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In this paper, we compare maximum likelihood (ML), quasi likelihood (QL) andweighted least squares (WLS) estimators for proportional error nonlinearregression models. Literature on thermoluminescence sedimentary dating revealedanother estimator similar to weighted least squares but observed responses usedas weights. This estimator that we refer to as data weighted least squares(DWLS) is also included in the comparison. We show that on the order $\sigma, $all four estimators behave similar to ordinary least squares estimators forstandard linear regression models. On the order of $\sigma^2, $ the estimatorshave biases. Formulae that are valid in the limit of small measurement errorare derived for the biases and the variances of the four estimators. Themaximum likelihood estimator has less bias compared to the quasi likelihoodestimator. Conditions are derived under which weighted least squares andmaximum likelihood estimators have similar biases. On the order of $\sigma^ {2}$, all estimators have similar standard errors. On higher order of $\sigma$,maximum likelihood estimator has smaller variance compared to quasi likelihoodestimator, provided that the random errors have the same first four moments asthe normal distribution. The maximum likelihood and quasi-likelihood estimatingequations are unbiased. In large samples, these two estimators are distributedas multivariate normal. The estimating equations for weighted least squares anddata weighted least squares are biased. However, in the limit of $\sigma \to 0$and $n \to \infty, $ if $ n^ {1/2} \sigma$ remains bounded, these twoestimators are also distributed as multivariate normal. A simulation studyjustified the applicability of the derived formulae in the presence ofmeasurement errors typical in sedimentary data. Results are illustrated with adata set from thermoluminescence sedimentary dating.

On comparison of estimators for proportional error nonlinear regression models in the limit of small measurement error