Mitigating the effect of measurement errors in quantile estimation

Quantiles are frequently used as descriptive measures. When data contains measurement errors, using the contaminated data to estimate the quantiles results in biased estimates. In this paper, we suggest two methods for reducing the effect of measurement errors on the quantile estimates and compare them, via an extensive simulation study, to the estimates obtained by the naive method, that is: by the estimates obtained from the observed (contaminated) data. The method we recommend is based on a method in a paper by Cook and Stefanski. However, we suggest using a combination of bootstrap and jackknifing to replace their extrapolation step.