The Modified Gauss-Newton Method for the Fitting of Non-Linear Regression Functions by Least Squares

Technometrics ◽  
1961 ◽  
Vol 3 (2) ◽  
pp. 269-280 ◽  
Author(s):  
H. O. Hartley
1980 ◽  
Author(s):  
Mark Heuser ◽  
Paul N. Somerville ◽  
Steven J. Bean

2020 ◽  
Vol 30 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Elena Moltchanova ◽  
Shirin Sharifiamina ◽  
Derrick J. Moot ◽  
Ali Shayanfar ◽  
Mark Bloomberg

AbstractHydrothermal time (HTT) models describe the time course of seed germination for a population of seeds under specific temperature and water potential conditions. The parameters of the HTT model are usually estimated using either a linear regression, non-linear least squares estimation or a generalized linear regression model. There are problems with these approaches, including loss of information, and censoring and lack of independence in the germination data. Model estimation may require optimization, and this can have a heavy computational burden. Here, we compare non-linear regression with survival and Bayesian methods, to estimate HTT models for germination of two clover species. All three methods estimated similar HTT model parameters with similar root mean squared errors. However, the Bayesian approach allowed (1) efficient estimation of model parameters without the need for computation-intensive methods and (2) easy comparison of HTT parameters for the two clover species. HTT models that accounted for a species effect were superior to those that did not. Inspection of credibility intervals and estimated posterior distributions for the Bayesian HTT model shows that it is credible that most HTT model parameters were different for the two clover species, and these differences were consistent with known biological differences between species in their germination behaviour.


2012 ◽  
Vol 182-183 ◽  
pp. 869-872
Author(s):  
Yan Ling Zhao ◽  
Xiao Shi Zheng ◽  
Guang Qi Liu ◽  
Na Li

LS-SVM (Least Squares Support Vector Machine) is simple and has a good ability of non-linear regression. As inputs of LS-SVM, DC-Energy-Ratio and Deviation of image samples are extracted first. Output of LS-SVM is the current texture classification. The results show that LS-SVM classifies images accurately by training the proposed two features.


2019 ◽  
Vol 20 (2) ◽  
pp. 83-92
Author(s):  
Małgorzata Kobylińska

This paper presents the application of the regression maximum depth for the estimation of linear regression function structural elements. For two-dimensional sets including untypical observations, regression functions were developed using the classical least squares method and a method based on the concept of observation depth measure in a sample. The effect of untypical observations on the estimated models has been noted.


2014 ◽  
Vol 7 (1) ◽  
pp. 69-97
Author(s):  
K. Tohsing ◽  
M. Schrempf ◽  
S. Riechelmann ◽  
G. Seckmeyer

Abstract. Spectral sky radiance (380–760 nm) is derived from measurements with a Hemispherical Sky Imager (HSI) system. The HSI consists of a commercial compact CCD (charge coupled device) camera equipped with a fish-eye lens and provides hemispherical sky images in three reference bands such as red, green and blue. To obtain the spectral sky radiance from these images non-linear regression functions for various sky conditions have been derived. The camera-based spectral sky radiance was validated by spectral sky radiance measured with a CCD spectroradiometer. The spectral sky radiance for complete distribution over the hemisphere between both instruments deviates by less than 20% at 500 nm for all sky conditions and for zenith angles less than 80°. The reconstructed spectra of the wavelength 380 nm to 760 nm between both instruments at various directions deviate by less then 20% for all sky conditions.


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