Pls regression is a recent technique that generalizes and combines features from principal component analysis and multiple regression. It is particularly useful when we need to predict a set of dependent variables from a (very) large set of independent variables (i.e., predictors). It originated in the social sciences (specifically economy, Herman Wold 1966) but became popular first in chemomet...

a simple and rapid method for the determination of 137ba isotope abundances in water samples by inductively coupled plasma-optical emission spectrometry (icp-oes) coupled with least-squares support vector machine regression (ls-svm) is reported. by evaluation of emission lines of barium, it was found that the emission line at 493.408 nm provides the best results for the determination of 137ba a...

Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of...

Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression models, using data encrypted under a fully homomorphic encryption scheme. Gradi...

A wide variety of neural and statistical methods are available for nonlinear empirical modeling based on different modeling approaches. Selecting the best method for a given task requires deep understanding of their similarities and differences and a systematic approach to method selection. This paper presents a common framework for gaining insight into neural and statistical modeling methods. ...

we present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step q-superlinear convergence. the approach is based on an adaptive structured scheme due to mahdavi-amiri and bartels of the exact penalty method of coleman and conn for nonlinearly constrained optimization problems. the structured adaptation also makes use of the ideas of n...

Sometimes, the relationship between an outcome (dependent) variable and the explanatory (independent) variable(s) is not linear. Restricted cubic splines are a way of testing the hypothesis that the relationship is not linear or summarizing a relationship that is too non-linear to be usefully summarized by a linear relationship. Restricted cubic splines are just a transformation of an independe...

The purpose of this paper is to present a new approach based on the Least Squares Error method for estimating the unknown parameters of the nonlinear 3rd order synchronous generator model. The proposed method uses the mathematical relationships between the machine parameters and on-line input/output measurements to estimate the parameters of the nonlinear state space model. The field voltage is...