## Quantifying the cost of simultaneous non-parametric
approximation of several samples

Given samples
we consider the problem of finding a function
, if any, which is simultaneously an adequate approximation for
all samples. Possible measures of cost are the number of local
extremes, the total variation of and its derivatives and the
supremum norm of derivatives of . The costs of a joint
approximation can be comparedwith the costs of approximating each
sample separately. The concept of approximation used is based on
the means of residuals
over a family of
subsets of intervals of .