Comparison of estimators of standard deviation for hydrologic time series
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Abstract
Unbiasing factors as a function of serial correlation, ρ, and sample size, n for the sample standard deviation of a lag one autoregressive model were generated by random number simulation. Monte Carlo experiments were used to compare the performance of several alternative methods for estimating the standard deviation σ of a lag one autoregressive model in terms of bias, root mean square error, probability of underestimation, and expected opportunity design loss. Three methods provided estimates of σ which were much less biased but had greater mean square errors than the usual estimate of σ: s = (1/(n - 1) ∑ (xi −x¯)2)½. The three methods may be briefly characterized as (1) a method using a maximum likelihood estimate of the unbiasing factor, (2) a method using an empirical Bayes estimate of the unbiasing factor, and (3) a robust nonparametric estimate of σ suggested by Quenouille. Because s tends to underestimate σ, its use as an estimate of a model parameter results in a tendency to underdesign. If underdesign losses are considered more serious than overdesign losses, then the choice of one of the less biased methods may be wise.
Suggested Citation
Tasker, G.D., Gilroy, E.J., 1982, Comparison of estimators of standard deviation for hydrologic time series: Water Resources Research, v. 18, no. 5, p. 1503-1508, https://doi.org/10.1029/WR018i005p01503.
ISSN: 1944-7973 (online)
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Comparison of estimators of standard deviation for hydrologic time series |
| Series title | Water Resources Research |
| DOI | 10.1029/WR018i005p01503 |
| Volume | 18 |
| Issue | 5 |
| Publication Date | July 09, 2010 |
| Year Published | 1982 |
| Language | English |
| Publisher | American Geophysical Union |
| Description | 6 p. |
| First page | 1503 |
| Last page | 1508 |