The two-to-one rule in data smoothing (Corresp.)
Athanasios Papoulis · IEEE Transactions on Information Theory · 1977
If a signal is estimated by a weighted average of the data in the interval(t - c, t + c ), then the variance\sigma^{2}of the estimate decreases, but its bias b increases, with increasing c. It is shown that in high accuracy estimates, the mean-square error e is minimum ifcis such that\sigma = 2b, regardless of the formh (t)of the smoothing weight. Furthermore, the resultinge_{m}is minimum ifh(t)is a truncated parabola.