Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity

Luminescence ◽  
2018 ◽  
Vol 33 (4) ◽  
pp. 742-750 ◽  
Author(s):  
Mohamed A. Korany ◽  
Azza A. Gazy ◽  
Essam F. Khamis ◽  
Marwa A. A. Ragab ◽  
Miranda F. Kamal
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Lipoic Acid ◽  
Weighted Least Squares ◽  
Fluorimetric Determination ◽  
Regression Methods ◽  
Least Median Of Squares ◽  
Robust Linear Regression

Simultaneous fluorimetric determination of acetylsalicylic acid metabolites in urine by partial least squares multivariate calibration

1995 ◽  
Vol 353 (2) ◽  
pp. 211-214 ◽  
Author(s):  
Arsenio Muñoz de la Peña ◽  
Isabel Durán-Merás ◽  
María D. Moreno ◽  
Francisco Salinas ◽  
María Martínez Galera
Keyword(s):  
Acetylsalicylic Acid ◽  
Least Squares ◽  
Partial Least Squares ◽  
Multivariate Calibration ◽  
Fluorimetric Determination ◽  
Acid Metabolites

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

Robust Weighted Least Squares Estimation of Regression Parameter in the Presence of Outliers and Heteroscedastic Errors

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Bello Abdulkadir Rasheed ◽  
Robiah Adnan ◽  
Seyed Ehsan Saffari ◽  
Kafi Dano Pati
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Robust Regression ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Model Parameters ◽  
Constant Variance ◽  
Regression Parameters ◽  
M Estimation

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

scholarly journals Application of artificial neural network to predict properties of diesel-biodiesel blends

1970 ◽  
Vol 6 (2) ◽  
pp. 98-103 ◽  
Author(s):  
Jatinder Kumar ◽  
Ajay Bansal
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Linear Regression ◽  
Least Squares ◽  
Statistical Technique ◽  
Training Algorithms ◽  
Biodiesel Blends ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

The experimental determination of various properties of diesel-biodiesel mixtures is very time consuming as well as tedious process. Any tool helpful in estimation of these properties without experimentation can be of immense utility. In present work, other tools of determination of properties of diesel-biodiesel blends were tried. A traditional statistical technique of linear regression (principle of least squares) was used to estimate the flash point, fire point, density and viscosity of diesel and biodiesel mixtures. A set of seven neural network architectures, three training algorithms along with ten different sets of weight and biases were examined to choose best Artificial Neural Network (ANN) to predict the above-mentioned properties of dieselbiodiesel mixtures. The performance of both of the traditional linear regression and ANN techniques were then compared to check their validity to predict the properties of various mixtures of diesel and biodiesel. Key words: Biodiesel; Artificial Neural Network; Principle of least squares; Diesel; Linear Regression. DOI: 10.3126/kuset.v6i2.4017Kathmandu University Journal of Science, Engineering and Technology Vol.6. No II, November, 2010, pp.98-103

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