Study on the biasedness of a regional log-linear estimator

Log-linear models are frequently used in hydrology, especially, for the regional estimation of flood volumes based on the physiographic data of a set of basins. A log-linear model describes a linear relationship between the log of a dependant variable and independent variables which are functions of parameters, of which the value remains to be determined. It is determined by using a set of basins with known values of dependant and independent variables. The model is then used to obtain a prediction for the dependant variable logarithm of a basin of interest, based on the known values of independent variables in the model. This prediction is unbiased with relation. to the log of the target variable. However, the exponential value of this prediction is biased with relation to the target variable. This paper addresses the measures to correct the bias in the prediction, which is introduced by exponentiation; the impacts on the variance of the ensuing predictions is also discussed.