Existence of the frequentistic estimate for power-law regression with a location parameter, with applications for making discharge rating curves |
| |
Authors: | Trond Reitan Asgeir Petersen-Øverleir |
| |
Institution: | (1) Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, 0316 Oslo, Norway;(2) Norwegian Water Resources and Energy Directorate, P. O. Box 5091, Majorstua, 0301 Oslo, Norway |
| |
Abstract: | Practical application of the power-law regression model with an unknown location parameter can be plagued by non-finite least squares parameter estimates. This presents a serious problem in hydrology, since stream flow data is mainly obtained using an estimated stage–discharge power-law rating curve. This study provides a set of sufficient requirements for the data to ensure the existence of finite least squares parameter estimates for a power-law regression with an unknown location parameter. It is shown that in practice, these requirements act as necessary for having a finite least squares solution, in most cases. Furthermore, it is proved that there is a finite probability for the model to produce data having non-finite least squares parameter estimates. The implications of this result are discussed in the context of asymptotic predictions, inference and experimental design. A Bayesian approach to the actual regression problem is recommended. |
| |
Keywords: | Power-law Location parameter Non-linear regression Least-squares Existence Stage– discharge rating curve |
本文献已被 SpringerLink 等数据库收录! |
|