Regression-quantile graduation of Australian life tables, 1946–1992

Regression-quantile methods developed since 1978 by Koenker and Bassett and others are being applied increasingly, especially by economists, to a wide variety of problems (e.g., Buchinsky, 1994; Manning et al., 1995). A prominent feature of these methods is the use of absolute deviation rather than squared deviation to measure lack of fit to data. The Schuette method of graduation, which can be seen as a special case of these methods, has not been used very much by actuaries. The purpose of this paper is to demonstrate the method via some examples, which may offer some insights into its advantages. Recently developed programs allow the graduator to find quickly the graduations for all values of the smoothing parameter, to view them serially as an aid to selecting one or more, and to obtain, in addition to the initial graduations (which are analogous to medians), estimates of the curves of conditional quantiles (e.g., 25th and 75th percentiles).