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.
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