NDLI: Existence of the frequentistic estimate for power-law regression with a location parameter, with applications for making discharge rating curves

Content Provider	Springer Nature Link
Author	Reitan, Trond Petersen Øverleir, Asgeir
Copyright Year	2006
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.
Starting Page	445
Ending Page	453
Page Count	9
File Format	PDF
ISSN	14363240
Journal	Stochastic Environmental Research and Risk Assessment
Volume Number	20
Issue Number	6
e-ISSN	14363259
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-07-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Power-law Location parameter Non-linear regression Least-squares Existence Stage–discharge rating curve Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution Math. Application in Environmental Science Numerical and Computational Methods in Engineering Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences Probability Theory and Stochastic Processes Math. Applications in Geosciences
Content Type	Text
Resource Type	Article
Subject	Environmental Chemistry Environmental Engineering Water Science and Technology Safety, Risk, Reliability and Quality

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