  We propose here a smooth estimator of the mean residual life function based
on randomly censored data. This is derived by smoothing the product-limit
estimator using the Chaubey-Sen technique (Chaubey and Sen (1998)). The
resulting estimator does not suffer from boundary bias as is the case with
standard kernel smoothing. The asymptotic properties of the estimator are
investigated. We establish strong uniform consistency and asymptotic normality.
This complements the work of Chaubey and Sen (1999) which considered a similar
estimation procedure in the case of complete data. It is seen that the
properties are similar, though technically more difficult to prove, to those in
the complete data case with appropriate modifications due to censoring.
