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Least-squares analysis of the Mueller matrix
Optics Letters, 2006In a single-mode fiber excited by light with a fixed polarization state, the output polarizations obtained at two different optical frequencies are related by a Mueller matrix. We examine least-squares procedures for estimating this matrix from repeated measurements of the output Stokes vector for a random set of input polarization states.
Michael, Reimer, David, Yevick
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Partial Least Squares: A First‐order Analysis
Scandinavian Journal of Statistics, 1998We compare the partial least squares (PLS) and the principal component analysis (PCA), in a general case in which the existence of a true linear regression is not assumed. We prove under mild conditions that PLS and PCA are equivalent, to within a first‐order approximation, hence providing a theoretical explanation for empirical findings reported by ...
Stoica, Petre, Söderström, Torsten
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Least-squares estimates in fuzzy regression analysis
European Journal of Operational Research, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kao, Chiang, Chyu, Chin-Lu
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Least Squares Methods of Analysis
1983In the first two contributions we have discussed the collection of single-photon decay data, which has been assumed undistorted by the excitation pulse — the assumption of a delta-pulse excitation. However, for decay times comparable in time-length to the excitation pulse this assumption is untrue, and we have an experimental result which is a ...
B. K. Selinger +2 more
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Least squares linear discriminant analysis
Proceedings of the 24th international conference on Machine learning, 2007Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. LDA in the binaryclass case has been shown to be equivalent to linear regression with the class label as the output. This implies that LDA for binary-class classifications can be formulated as a least squares problem.
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[16] Nonlinear least-squares analysis
1985Publisher Summary This chapter highlights one of the methods for the analysis of experimental data, along with the assumptions, advantages, and disadvantages of the method. The most important experimental detail to understand for any parameter estimation procedure is the sources and magnitudes of the random and nonrandom experimental errors ...
Michael L. Johnson, Susan G. Frasier
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Collinearity in Least-Squares Analysis
Journal of Chemical Education, 2011How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions ...
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Linearized least-squares data analysis
The Journal of the Acoustical Society of America, 1993One of the most attractive features of many acoustic teaching laboratory experiments is their ability to produce high-quality (precision) data. This affords the possibility of also using the results of these laboratory exercises to teach advanced techniques for data analysis that exploit the ubiquity of least-squares data analysis routines which are ...
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Recursive Least Squares Regression Analysis
1984The recursive least squares (RLS) algorithm II developed in the previous Chapter provides a general method of estimating the parameters in a multi-parameter regression model. But, as we have pointed out, the algorithm is a deterministic estimation procedure in the sense that it makes few assumptions about either the statistical nature of the signals or
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Partial Least Squares Path Analysis
2015We begin our review of modern path analysis tools with partial least squares path analysis software. PLS-PA has achieved near-cult-like stature within its circle of practitioners, but is not without its critics. Many issues arise from PLS-PA not being a proper statistical “methodology”—it has failed to accumulate a body of statistical research on ...
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