The two-to-one rule in data smoothing (Corresp.)

If a signal is estimated by a weighted average of the data in the interval , then the variance 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 if is such that , regardless of the form of the smoothing weight. Furthermore, the resulting is minimum if is a truncated parabola.