Curve fits in the presence of random and systematic error

American Journal of Physics

Volumn 68, Issue 5, 2000, Pages 424-429

  Bechhoefer, John ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034395412     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19457     Document Type: Article

References (13)

1. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), 2nd ed., pp. 194-219.
2. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing (Cambridge U.P., Cambridge, 1992), 2nd ed., pp. 650-700.
3. In this paper, I follow the statistics literature and denote the quantity γ(j) defined in Eq. (4) as the autocovariance function. In the physics literature, this quantity is often called the autocorrelation function, which properly refers only to the case where the function is normalized such that γ(0) = 1. The definition of both quantities would be slightly different if the mean of the residuals were not zero.
4. The intensity-intensity correlation light-scattering data represent an autocorrelation function, too. This is, of course, a different quantity from the autocovariance of residuals discussed in this paper.
5. -1 in the free case.
6. A note of caution: If the y; are nonlinear transforms of normally distributed data, then the errors in y are no longer normal. In such a case, the least-squares fitting algorithm can lead to biased estimates of parameters. One can generalize the algorithm by going back to its starting point based on maximizing the likelihood function. For a discussion of this and related points, see J. R. Macdonald and W. J. Thompson, "Strongly heteroscedastic nonlinear regression," Commun. Stat.-Simul. Comput. 20, 843-886 (1991).
7. K. Dutton, S. Thompson, and B. Barraclough, The Art of Control Engineering (Addison-Wesley, Harlow, England, 1997), pp. 413-427.
8. C. Chatfield, The Analysis of Time Series: An Introduction (Chapman and Hall, London, 1996), 5th ed., pp. 61-63.
9. D. R. Wittink, The Application of Regression Analysis (Allyn and Bacon, Needham Heights, MA, 1988), pp. 175-198.
10. A. Stuart, J. K. Ord, and S. Arnold, Kendall's Advanced Theory of Statistics, Classical Inference and the Linear Model, Vol. 2A (Arnold, London, 1999), 6th ed., Chap. 25.
11. Other common statistics references for physical scientists include W. T. Eadie, D. Drijard, F. E. James, M. Roos, and B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971); L. Lyons, Statistics for Nuclear and Particle Physics (Cambridge U.P., Cambridge, 1986); and G. Cowan, Statistical Data Analysis, with Applications from Particle Physics (Oxford U.P., Oxford, 1998).
12. Other common statistics references for physical scientists include W. T. Eadie, D. Drijard, F. E. James, M. Roos, and B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971); L. Lyons, Statistics for Nuclear and Particle Physics (Cambridge U.P., Cambridge, 1986); and G. Cowan, Statistical Data Analysis, with Applications from Particle Physics (Oxford U.P., Oxford, 1998).
13. Other common statistics references for physical scientists include W. T. Eadie, D. Drijard, F. E. James, M. Roos, and B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971); L. Lyons, Statistics for Nuclear and Particle Physics (Cambridge U.P., Cambridge, 1986); and G. Cowan, Statistical Data Analysis, with Applications from Particle Physics (Oxford U.P., Oxford, 1998).