Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene
Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene
Publications and Research
The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.
Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene
Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene
Publications and Research
This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.