  A reduced-bias nonparametric estimator of the cumulative distribution
function (CDF) and the survival function is proposed using infinite-order
kernels. Fourier transform theory on generalized functions is utilized to
obtain the improved bias estimates. The new estimators are analyzed in terms of
their relative deficiency to the empirical distribution function and
Kaplan-Meier estimator, and even improvements in terms of asymptotic relative
efficiency (ARE) are present under specified assumptions on the data. The
deficiency analysis introduces a deficiency rate which provides a continuum
between the classical deficiency analysis and an efficiency analysis.
Additionally, an automatic bandwidth selection algorithm, specially tailored to
the infinite-order kernels, is incorporated into the estimators. In small
sample sizes these estimators can significantly improve the estimation of the
CDF and survival function as is illustrated through the deficiency analysis and
computer simulations.
