thumbnail

Comparison of estimators of standard deviation for hydrologic time series

Water Resources Research

By:
and
https://doi.org/10.1029/WR018i005p01503

Links

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 )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.

Additional publication details

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