Modelling and analysis of data that exhibit temporal decay

Two recent examples of data from statistical consulting work form the basis of this paper. Both data sets arose from situations where temporal decay was expected, and different models for this are discussed, in particular, variants on simple exponential decay: hyperexponential (or mixed exponential) decay and models based on differential equations. Nonparametric estimation, using local quadratic smoothing of the data, of components of these models is discussed and employed to help to check the appropriateness or otherwise of existing parametric analyses of the data. In one example, the suitability of the parametric analysis is confirmed; in the other, the parametric assumptions made at the time are shown to have some flaws, and an improved parametric analysis is provided.