Analysis of neutrosophic multiple regression

The idea of Neutrosophic statistics is utilized for the analysis of the uncertainty observation data. Neutrosophic multiple regression is one of a vital roles in the analysis of the impact between the dependent and independent variables. The Neutrosophic regression equation is useful to predict the future value of the dependent variable. This paper to predict the students' performance in campus interviews is based on aptitude and personality tests, which measures conscientiousness, and predict the future trend. Neutrosophic multiple regression is to authenticate the claim and examine the null hypothesis using the F-test. This study exhibits that Neutrosophic multiple regression is the most efficient model for uncertainty rather than the classical regression model

Variable selection in multiple regression with random design

We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and dimensionality. Then, estimators for these parameters are proposed and the resulting method for selecting variables is shown to be consistent. A simulation study that permits to gain understanding of the performances of the proposed approach and to compare it with an existing method is given

Lasso Estimation of an Interval-Valued Multiple Regression Model

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried out by transforming a quadratic optimization problem with inequality constraints into a linear complementary problem and using Lemke's algorithm to solve it. Due to the irrelevance of certain cross-relationships, an alternative estimation process, the LASSO (Least Absolut Shrinkage and Selection Operator), is developed. A comparative study showing the differences between the proposed estimators is provided

Optimal method in multiple regression with structural changes

In this paper, we consider an estimation problem of the regression coefficients in multiple regression models with several unknown change-points. Under some realistic assumptions, we propose a class of estimators which includes as a special cases shrinkage estimators (SEs) as well as the unrestricted estimator (UE) and the restricted estimator (RE). We also derive a more general condition for the SEs to dominate the UE. To this end, we generalize some identities for the evaluation of the bias and risk functions of shrinkage-type estimators. As illustrative example, our method is applied to the "gross domestic product" data set of 10 countries whose USA, Canada, UK, France and Germany. The simulation results corroborate our theoretical findings.Comment: Published at http://dx.doi.org/10.3150/14-BEJ642 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm