Nittaya McNeil, Patarapan Odton, and Attachai Ueranantasun

pp. 117 - 120

Abstract

Spline functions have been suggested in demographic research for interpolating age-specific data as they have desirable smoothness optimality properties. However, difficulties arise when boundary conditions need to be satisfied. An
additional problem is that age-specific demographic data functions are necessarily non-negative, requiring the interpolating
spline to be monotonic non-decreasing. In this paper we describe a simple and effective alternative that circumvents these
problems. We show that natural cubic splines can be used to interpolate age-specific demographic data and ensure that
relevant boundary conditions on second derivatives are satisfied, thus preserving the desirable optimality property of the
interpolating function without the need to increase the degree of the spline function. The method involves incorporating one
or two additional strategically placed knots with values estimated from the data. We describe how the method works for
selected fertility, population, and mortality data.