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.
| 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 |
| Year Published | 1982 |
| Language | English |
| Publisher | American Geophysical Union |
| Description | 6 p. |
| First page | 1503 |
| Last page | 1508 |
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