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Comparison of estimators of standard deviation for hydrologic time series
Author(s) -
Tasker Gary D.,
Gilroy Edward J.
Publication year - 1982
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr018i005p01503
Subject(s) - statistics , standard deviation , estimator , mathematics , autoregressive model , series (stratigraphy) , mean squared error , monte carlo method , nonparametric statistics , sample size determination , standard error , lag , econometrics , computer science , paleontology , computer network , biology
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) ∑ ( x i − 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.