Algorithm 376: Least squares fit by f(x) = A cos (B x + C [E2]

1970 ◽  
Vol 13 (2) ◽  
pp. 121-122 ◽  
Author(s):  
H. Späth
Keyword(s):  
Least Squares ◽  
Least Squares Fit

Changes in total body calcium balance with exercise in the rat

1983 ◽  
Vol 55 (1) ◽  
pp. 201-204 ◽  
Author(s):  
A. D. LeBlanc ◽  
H. J. Evans ◽  
P. C. Johnson ◽  
S. Jhingran
Keyword(s):  
Least Squares ◽  
Voluntary Exercise ◽  
Calcium Balance ◽  
Sprague Dawley ◽  
Total Body Calcium ◽  
Sprague Dawley Rats ◽  
Least Squares Fit ◽  
Significant Change ◽  
Total Body ◽  
And Control

The purpose of this study was to evaluate the effect of deconditioning on the total body calcium in rats. Two separate experiments were performed using female Sprague-Dawley rats, 187-266 days of age. Total body calcium was measured in experimental and control rats during and following several weeks of voluntary exercise. The slope from the least-squares fit of total body calcium with time was used to obtain an average calcium balance for each animal during each study period. In both groups the exercised rats had a significantly decreased calcium balance after cessation of exercise, whereas no significant change was seen in nonexercised controls. In both groups, the exercised animals gained calcium at a significantly greater rate than controls. Our findings indicate that while exercised rats may gain calcium at a faster rate compared with nonexercising controls, the rate of gain following cessation of exercise is less than the controls.

Estimation of the free core nutation period by the sliding-window complex least-squares fit method

2016 ◽  
Vol 57 (10) ◽  
pp. 2136-2140 ◽  
Author(s):  
Yonghong Zhou ◽  
Qiang Zhu ◽  
David A. Salstein ◽  
Xueqing Xu ◽  
Si Shi ◽  
...  
Keyword(s):  
Least Squares ◽  
Sliding Window ◽  
Free Core Nutation ◽  
Least Squares Fit

scholarly journals A Robust Regression by Using Huber Estimator and Tukey Bisquare Estimator for Predicting Availability of Corn in Karanganyar Regency, Indonesia

2018 ◽  
Vol 1 (1) ◽  
pp. 37
Author(s):  
Hasih Pratiwi ◽  
Yuliana Susanti ◽  
Sri Sulistijowati Handajani
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Likelihood Estimation ◽  
Corn Production ◽  
Least Squares Fit ◽  
Class Of Estimators ◽  
M Estimation ◽  
Heavy Tailed ◽  
Least Squares Estimates ◽  
Huber Estimator

Linear least-squares estimates can behave badly when the error distribution is not normal, particularly when the errors are heavy-tailed. One remedy is to remove influential observations from the least-squares fit. Another approach, robust regression, is to use a fitting criterion that is not as vulnerable as least squares to unusual data. The most common general method of robust regression is M-estimation. This class of estimators can be regarded as a generalization of maximum-likelihood estimation. In this paper we discuss robust regression model for corn production by using two popular estimators; i.e. Huber estimator and Tukey bisquare estimator.<br />Keywords : robust regression, M-estimation, Huber estimator, Tukey bisquare estimator

A Wind Wave Co-Cumulative Spectral Model

1970 ◽  
Vol 14 (04) ◽  
pp. 277-295
Author(s):  
Carl F. Kottler
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Wind Velocity ◽  
Wind Wave ◽  
Surface Wind ◽  
Systematic Investigation ◽  
Spectral Model ◽  
Least Squares Fit ◽  
Wind Sea ◽  
Cumulative Model

A systematic investigation was made of the parameters chosen to define the Pierson-Moskowitz wind sea spectral model. The model was generalized and the form was extended to give a better fit of the data. Using the same sets of data as those selected by Pierson and Moskowitz for building their model, a least-squares fit of each set of the co-cumulative data gave a corresponding optimum set of parameters. These unique optimum sets of parameters yielded an eightfold decrease in the standard deviation. From this family of parameter sets, a co-cumulative spectral model was. developed to fix some of the parameters and relate the others to surface wind velocity. This modification and extension show that at least a twofold improvement in accuracy over the associated Pierson-Moskowitz co-cumulative model can be achieved.

Model misspecification and bias in the least-squares algorithm: Implications for linearized isotropic AVO

2021 ◽  
Vol 40 (9) ◽  
pp. 646-654
Author(s):  
Henning Hoeber
Keyword(s):  
Least Squares ◽  
Model Misspecification ◽  
Forward Model ◽  
Model Parameters ◽  
Omitted Variables ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Omitted Variable Bias ◽  
Least Squares Fit ◽  
Variable Bias

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the χ-angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.

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