REGIONAL HYDROLOGIC ANALYSIS - ORDINARY AND GENERALIZED LEAST-SQUARESREVISITED

Generalized least squares (GLS) regional regression procedures have be en developed for estimating river flow quantiles. A widely used GLS pr ocedure employs a simplified model error structure and average covaria nces when constructing an approximate residual error covariance matrix . This paper compares that GLS estimator (<(beta)over bar>(MC)(GLS), a n idealized GLS estimator (<(beta)over bar>(E)(GLS)) based on the simp lifying assumptions of <(beta)over bar>(MC)(GLS) with true underlying statistics in a region, the best possible GLS estimator (<(beta)over b ar>(T)(GLS)) obtained using the true residual error covariance matrix, and the ordinary least squares estimator (<(beta)over bar>(T)(OLS)). Useful analytic expressions are developed for the variance of <(beta)o ver bar>(T)(GLS), <(beta)over bar>(E)(GLS), and <(beta)over bar>(T)(OL S). For previously examined cases the average sampling mean square err or (mse(s)) of <(beta)over bar>(T)(GLS), and the mse(s) of <(beta)over bar>(MC)(GLS) usually was larger than the mse(s) of both <(beta)over bar>(E)(GLS) and <(beta)over bar>(T)(GLS). The loss in efficiency of < (beta)over bar>(MC)(GLS) was mostly due to estimating streamflow stati stics employed in the construction of the residual error covariance ma trix rather than the simplifying assumptions in presently employed GLS estimators. The new analytic expressions were used to compare the per formance of the OLS and GLS estimators for new cases representing grea ter model variability across sites as well as the effect return period has oil the estimators' relative performance. For a more heteroscedas tic model error variance and larger return periods, some increase in t he mse(s) of <(beta)over bar>(E)(GLS) relative to the mse(s) <(beta)ov er bar>(T)(GLS) was observed.