Univariate graduation of mortality by local polynomial regression

Life tables are used to describe the one-year probability of death within a well defined population as a function of attained age. These probabilities play an important role in the determination of premium rates and reserves in life insurance. The crude estimates on which life tables are based might be considered as a sample from larger population and are, as a result, subject to random fluctuations. However, the actuary wishes most of the time to smooth these quantities to enlighten the characteristics of the mortality of the group considered which he thinks to be relatively regular.
The present article discusses a non-parametric graduation method of experience data originating from life insurance. We introduce local univariate polynomial regression. We discuss the choices of the smoothing parameters and criteria used for models selection. We graduate the mortality data through the choice of the smoothing parameters. The graduation and corresponding confidence intervals are carried over the entire age range. Tests are used to compare the graduated rates obtained by local polynomial regression with those obtained by the Whittaker-Henderson smoothing.