  Mortality is different across countries, states and regions. Several
empirical research works however reveal that mortality trends exhibit a common
pattern and show similar structures across populations. The key element in
analyzing mortality rate is a time-varying indicator curve. Our main interest
lies in validating the existence of the common trends among these curves, the
similar gender differences and their variability in location among the curves
at the national level. Motivated by the empirical findings, we make the study
of estimating and forecasting mortality rates based on a semi-parametric
approach, which is applied to multiple curves with the shape-related nonlinear
variation. This approach allows us to capture the common features contained in
the curve functions and meanwhile provides the possibility to characterize the
nonlinear variation via a few deviation parameters. These parameters carry an
instructive summary of the time-varying curve functions and can be further used
to make a suggestive forecast analysis for countries with barren data sets. In
this research the model is illustrated with mortality rates of Japan and China,
and extended to incorporate more countries.
