Edward J. Gilroy Gary D. Tasker 1982 <p><span>Unbiasing factors as a function of serial correlation,&nbsp;</span><i>ρ</i><span>, and sample size,<span>&nbsp;</span></span><i>n</i><span><span>&nbsp;</span>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:<span>&nbsp;</span></span><i>s</i><span><span>&nbsp;</span>= (1/(</span><i>n</i><span><span>&nbsp;</span>- 1) ∑ (</span><i>x</i>_<i>i</i><span><span>&nbsp;</span>−</span><i>x¯</i><span>)</span>²<span>)</span>^½<span>. 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<span>&nbsp;</span></span><i>s</i><span><span>&nbsp;</span>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.</span></p> application/pdf 10.1029/WR018i005p01503 en American Geophysical Union Comparison of estimators of standard deviation for hydrologic time series article