The Fitting of Power Series,Meaning Polynomials,Illustrated on Band-Spectroscopic Data |
| |
Authors: | Albert E Beaton John W Tukey |
| |
Affiliation: | 1. Princeton University, Educational Testing Service , Princeton , New Jersey;2. Princeton University, Bell Laboratories , Princeton and Murray Hill , New Jersey |
| |
Abstract: | The prototype of fitting polynomials to equally-spaced data—in which the equalspacing is theoretically precise and the data is accurate to many decimal places—arises in the analysis of band spectra. A hard look at such examples forces us to reexamine our thinking on such diverse issues as: How to formulate such problems, the use of robust/resistant techniques in polynomial regression, which coordinates to use and why, the basic properties of linear least squares, choices in stopping a fit, and improved ways to describe our answers. Our results and attitudes apply rather directly to other situations where we are fitting a sum of functions of a single variable. When two or more different variables, subject to error, blunder, or omission, underlie the carriers to be considered, regression/fitting problems are likely to need not only the considerations presented here, but others as well. To a varying extent, the same will be true of nonlinear fitting/regression problems. |
| |
Keywords: | Regression Polynomial Regression Fitting Polynomial Fitting Fitting and Band-Spectroscopic Data Robust/Resistant Regression SMOFIT Regression Biweights Regression Least Squares Effects of Imprecise Weighting Carriers Catchers Usable Fractions Fitting Non-Polynomials with Polynomials Stopping Fitting Orthogonality vs Biorthogonality Balancing Bias and Variance Minvar Modification Describing Variability of Vector Estimates Resistant Non-Linear Smoothers |
|
|