Computing ordinary least-squares parameter estimates for the National Descriptive Model of Mercury in Fish
Techniques and Methods
7-C10
This report is Chapter 10 of Section C: Computer programs in Book 7 Automated Data Processing and Computations
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Abstract
A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products X'X and X'y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce X'X and X'y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8p2+16p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software.
| Publication type | Report |
|---|---|
| Publication Subtype | USGS Numbered Series |
| Title | Computing ordinary least-squares parameter estimates for the National Descriptive Model of Mercury in Fish |
| Series title | Techniques and Methods |
| Series number | 7-C10 |
| DOI | 10.3133/tm7C10 |
| Year Published | 2013 |
| Language | English |
| Publisher | U.S. Geological Survey |
| Publisher location | Reston, VA |
| Contributing office(s) | Eastern Geographic Science Center |
| Description | iii, 9 p.; Appendix |
| Larger Work Type | Report |
| Larger Work Subtype | USGS Numbered Series |
| Larger Work Title | Section C: Computer programs in Book 7 Automated Data Processing and Computations |
| Online Only (Y/N) | Y |
| Additional Online Files (Y/N) | Y |
| Google Analytic Metrics | Metrics page |