Estimation of the mean residual life function in the presence of measurement errors

The data available for statistical analysis from many scientific areas often come with measurement error. Ignoring measurement error can bring forth biased estimates and lead to erroneous conclusions to various degrees in a data analysis. This paper considers the problem of estimation of the mean residual life function assuming that observed lifetime random variables are given by a multiplicative measurement error model. The consistency of the estimator are proven under some regularity conditions. It is also shown that the estimator weakly converges to a normal distribution. Finally, numerical examples based on an extensive simulation study and real lifetime data analysis are presented to illustrate the theory and assess performance of the estimator.