Bounds for how much influence an observation can have

That outliers or influential observations can affect the results in a regression is well-known. But it is not clear how much influence a specific observation can have on other statistics. In time series, especially in predictive situations, the effect of additional observations is of singular importance. We here examine bounds for the effect of an additional observation on the mean, variance, Mahalanobis distance, product moment correlation, and coefficients of linearity and monotonicity.