Abstract 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.

中文翻译：

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非平稳条件下条件均值估计量的比较

摘要 人们越来越关注开发用于洪水、干旱和其他水文过程的非平稳频率分析 (NFA) 的无数复杂方法。我们假设对 NFA 的需求源于众所周知的确定性变化机制。这里受到质疑的 NFA 中的一个常见假设是，当采用更现实、复杂和复杂的模型时，会产生更准确的水文统计估计值。通过考虑年平均洪水（干旱或其他水文事件），当样本平均值 (SM) 是比平均值 (RM) 的回归估计更有效（更低的均方误差，MSE）估计量时，可以得出一般条件。我们引入了一个最优分数平均估计量 FM*，它只是最近记录 nf* 时期的 SM，其中 f* 是完整样本 n 的最佳部分，这导致 f 的所有可能值中的最小 MSE。有趣的是，在与拟合回归模型相关的显着性水平超过约 0.05 时，FM* 通常优于 RM。鉴于围绕潜在非平稳条件的大量关注和不确定性，我们证明了利用历史记录的最佳近期子集的简约估计量可能比通常提倡的许多更复杂的非平稳方法更具吸引力。