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Inconsistent matrices in estimating ungaged streamflow data
Author(s) -
Fuller G. A.,
Fuller N. E.
Publication year - 1974
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/wr010i006p01249
Subject(s) - mathematics , statistics , correlation , streamflow , range (aeronautics) , least squares function approximation , geography , drainage basin , materials science , geometry , cartography , estimator , composite material
Least squares estimated correlation coefficients between gaged and ungaged streams are sometimes used in the estimation of ungaged streamflow. Constructed correlation matrices containing actual and estimated correlation coefficients may not be positive semidefinite and thus may cause computational problems. To overcome this problem, an algorithm, based on Rosenbrock's hill‐climbing technique, was used. The maximum absolute deviation from the least squares estimates was minimized subject to the constraints that each leading principal minor be nonnegative and that the correlation coefficients must lie within the range −1.0 to 1.0 inclusive. With this algorithm, only the estimated correlation coefficients are modified.