Multicollinearity and A Ridge Parameter Estimation Approach

One of the main goals of the multiple linear regression model, Y = Xβ + u, is to assess the importance of independent variables in determining their predictive ability. However, in practical applications, inference about the coefficients of regression can be difficult because the independent variables are correlated and multicollinearity causes instability in the coefficients. A new estimator of ridge regression parameter is proposed and evaluated by simulation techniques in terms of mean squares error (MSE). Results of the simulation study indicate that the suggested estimator dominates ordinary least squares (OLS) estimator and other ridge estimators with respect to MSE

Ridge Regression and Ill-Conditioning

Hoerl and Kennard (1970) suggested the ridge regression estimator as an alternative to the Ordinary Least Squares (OLS) estimator in the presence of multicollinearity. This article proposes new methods for estimating the ridge parameter in case of ordinary ridge regression. A simulation study evaluates the performance of the proposed estimators based on the Mean Squared Error (MSE) criterion and indicates that, under certain conditions, the proposed estimators perform well compared to the OLS estimator and another well-known estimator reviewed

Theoretical and numerical analysis of a coupled system of second order non-linear differential equations

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented

Numerical analysis of a model for Nickel-Iron alloy electrodeposition on rotating disk electrode

International audienceTo better understand the nickel-iron electrodeposition process, we have developed one-dimensional numerical model. This model addresses dissociation, diffusion, electromigration, convection and deposition of multiple ion species.\ The reaction mechanism in this model differs in that $$ and $Fe^{2+}$ are the electroactive species and $NiOH^{+}$ and $$ are not involved whatsover.\ To take account of the anisot-ropic behaviour of the solution we introduce a domain decomposition numerical method. Simulations with experimental data shows that our model can predict characteristic features of the nickel-iron system

Topological derivatives for semilinear elliptic equations

International audienceThe form of topological derivatives for integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the $L^{\infty}$ norm are obtained. Results of numerical experiments which confirm the theoretical convergence rate are presented

Bifurcation for systems involving Lipschitz continuous mappings at multiple eigenvalues

Some results on the existence of bifurcation at multiple eigenvalues for abstract systems concerning Lipschitz continuous mappings in Banach spaces are proved. The obtained results improve some wellknown bifurcation results by Crandall and Rabinowitz, McLeod and Sattinger, Tan etc, in the case involving Lipschitz continuous mappings. An application to a system of partial differential equations will be given