• Demographic rates
• German districts
• mortality rates
• Population projection
• Smoothing methods
• Splines.

Population projection and indeed accurate demographic projections are essential for effective policymaking and resource allocation. Demographic rates such as births, deaths, and migration, are essential indicators for understanding population dynamics. Yet, small area rates often show high noise, variability, and instability, necessitating the application of smoothing techniques to enhance reliability and precision. It is under this background that this thesis is intended to examine different smoothing methods employed in the domain of demographic rates, with a specific focus on their application to small geographic areas.
The study used TOPALS - "Tool for projecting age patterns using linear splines", P-TOPALS - "Penalised Tool for Population Analysis with Linear Splines", P-splines, General Additive (Mixed) Models (GAMM), and Bayesian methods to smooth mortality rates. These methods were evaluated for their ability to be smooth in different settings. These were mostly focused on the computational efficiency, shape similarity, goodness of fit, and plausibility of the resulting estimates.
The national mortality rate of Germany was used to simulate district-level mortality data and death counts and was subsequently aggregated into specific age groups. This dataset provided a strong basis for testing the smoothing methods under varying conditions, paving the way for a comprehensive assessment of each technique's performance across the different setups. The simulations were conducted by assuming different scenarios.
The results highlight the strengths and weaknesses of each smoothing method. For instance, TOPALS proved effective in establishing a good fit in all setups followed by P-TOPALS and P-spline. Whereas the GAMM method excelled at establishing a smoother shape together with the Bayesian approach which offers a balance between smoothness and computational efficiency. In the end, no method attained both fitness and smoothness in all scenarios; however, a balance between the two was prevalent. This implies that there is no one-size-fits-all method for all scenarios. The TOPALS duos and P-spline demonstrated strong overall fit, whereas GAMM and the Bayesian approach excelled in smoothness. The results underscore the need for a careful balance between these two criteria when selecting a smoothing method.