Revisiting Whittaker-Henderson Smoothing

Origin

Whittaker-Henderson (WH) smoothing is a graduation method designed to mitigate the effects of sampling fluctuations in a vector of evenly spaced discrete observations. Although this method was originally proposed by Bohlmann (1899), it is named after Whittaker (1923), who applied it to graduate mortality tables, and Henderson (1924), who popularized it among actuaries in the United States. The method was later extended to two dimensions by Knorr (1984). WH smoothing may be used to build experience tables for a broad spectrum of life insurance risks, such as mortality, disability, long-term care, lapse, mortgage default and unemployment.

The one-dimensional case

Let