Abstract
•The conditional or current mean is widely needed in nonstationary frequency analysis.•Optimal fractional mean FM*, is the mean of a recent subset of record with minimum mean square error.•FM* is preferred to regression and sample means under a very wide range of conditions.•A decision rule is developed for estimator choice under nonstationary conditions.
There is increasing attention to the development of a myriad of complex methods for nonstationary frequency analysis (NFA) of floods, droughts and other hydrologic processes. We assume that the need for NFA arises from well understood deterministic mechanisms of change. A common assumption in NFA, questioned here, is that more accurate estimators of hydrologic statistics result when more realistic, complex and sophisticated models are employed. By considering the mean annual flood (drought or other hydrologic event), general conditions are derived when the sample mean (SM) is a more efficient (lower mean square error, MSE) estimator than a regression estimate of the mean (RM). We introduce an optimal fractional mean estimator, FM*, which is simply the SM of the most recent period of record nf*, where f* is the optimal fraction of the full sample n, which leads to minimum MSE among all possible values of f. Interestingly, FM* is generally preferred over RM for attained significance levels associated with the fitted regression model in excess of about 0.05. Given the considerable attention and uncertainty surrounding potential nonstationary conditions, we demonstrate that a parsimonious estimator which exploits an optimal recent subset of the historical record may be more attractive than many of the more complex nonstationary approaches commonly advocated.