Iteratively reweighted least squares: A comparison of several single step algorithms for linear models

1992 ◽  
Vol 32 (3) ◽  
pp. 506-524 ◽  
Author(s):  
Ralf Wolke
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Single Step ◽  
Iteratively Reweighted Least Squares

The use of linear models and matrix least squares in clinical chemistry.

1979 ◽  
Vol 25 (6) ◽  
pp. 840-855 ◽  
Author(s):  
S N Deming ◽  
S L Morgan
Keyword(s):  
Least Squares ◽  
Precise Measurement ◽  
Linear Models ◽  
Clinical Chemistry ◽  
Experimental Designs ◽  
Unified Approach

Abstract We present a unified approach to the use of linear models and matrix least squares with the intention of providing a better understanding of the techniques themselves and of the statistics that arise from these techniques as they are used in clinical chemistry. Emphasis is placed on the importance of appropriate experimental designs and adequately precise measurement processes for efficiently obtaining the desired information.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

Functional Linear Regression

2018 ◽  
Author(s):  
Hervé Cardot ◽  
Pascal Sarda
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
Principal Component Regression ◽  
Principal Component ◽  
Penalized Least Squares ◽  
Open Problems ◽  
Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

scholarly journals Analytical quality assessment of iteratively reweighted least-squares (IRLS) method

2014 ◽  
Vol 20 (1) ◽  
pp. 132-141 ◽  
Author(s):  
Jianfeng Guo
Keyword(s):  
Least Squares ◽  
Order Approximation ◽  
Diagnostic Tools ◽  
Iteratively Reweighted Least Squares ◽  
First Order ◽  
Iterative Reweighting ◽  
First Order Approximation ◽  
Detectable Bias ◽  
Theoretical Analyses ◽  
Exact Analytical Method

The iteratively reweighted least-squares (IRLS) technique has been widely employed in geodetic and geophysical literature. The reliability measures are important diagnostic tools for inferring the strength of the model validation. An exact analytical method is adopted to obtain insights on how much iterative reweighting can affect the quality indicators. Theoretical analyses and numerical results show that, when the downweighting procedure is performed, (1) the precision, all kinds of dilution of precision (DOP) metrics and the minimal detectable bias (MDB) will become larger; (2) the variations of the bias-to-noise ratio (BNR) are involved, and (3) all these results coincide with those obtained by the first-order approximation method.

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