Ordinary least square regression, orthogonal regression, geometric mean regression and their applications in aerosol science

Ordinary Least Square Regression, Orthogonal Regression, Geometric Mean Regression and their Applications in Aerosol Science

Abstract. Regression analysis, especially the ordinary least squares method which assumes that errors are confined to the dependent variable, has seen a fair share of its applications in aerosol science. The ordinary least squares approach, however, could be problematic due to the fact that atmospheric data often does not lend itself to calling one variable independent and the other dependent. ...

Orthogonal Least Square with Boosting for Regression

Partial Least Square Regression PLS-Regression

PLS regression is a recent technique that generalizes and combines features from principal component analysis and multiple regression. Its goal is to predict or analyze a set of dependent variables from a set of independent variables or predictors. This prediction is achieved by extracting from the predictors a set of orthogonal factors called latent variables which have the best predictive pow...

Orthogonal Nonlinear Least-Squares Regression in R

Orthogonal nonlinear least squares (ONLS) regression is a not so frequently applied and largely overlooked regression technique that comes into question when one encounters an ”error in variables” problem. While classical nonlinear least squares (NLS) aims to minimize the sum of squared vertical residuals, ONLS minimizes the sum of squared orthogonal residuals. The method is based on finding po...

Learning Rates of Least-Square Regularized Regression

This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and the capacity of the reproducing kernel Hilbert...