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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.

Additional Publication Details

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
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