Mathematics and Statistics 11(1): 51-64, 2023 DOI: 10.13189/ms.2023.110106 http://www.hrpub.org Raise Estimation: An Alternative Approach in The Presence of Problematic Multicollinearity Jinse Jacob, R. Varadharajan * Department of Mathematics, SRM Institute of Science and Technology, India Received August 8, 2022; Revised November 21, 2022; Accepted December 22, 2022 Cite This Paper in the following Citation Styles (a): [1] Jinse Jacob, R. Varadharajan, ”Raise Estimation: An Alternative Approach in The Presence of Problematic Multicollinearity,” Mathematics and Statistics, Vol.11, No.1, pp. 51-64, 2023. DOI: 10.13189/ms.2023.110106 (b): Jinse Jacob, R. Varadharajan, (2023). Raise Estimation: An Alternative Approach in The Presence of Problematic Multicollinearity. Mathematics and Statistics, 11(1), 51-64. DOI: 10.13189/ms.2023.110106 Copyright ©2023 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract When adopting the Ordinary Least Squares (OLS) method to compute regression coefficients, the results become unreliable when two or more predictor variables are linearly related to one another. The confidence interval of the estimates becomes longer as a result of the increased variance of the OLS estimator, which also causes test procedures to have the potential to generate deceptive results. Additionally, it is difficult to determine the marginal contribution of the associated predictors since the estimates depend on the other predictor variables that are included in the model. This makes the determination of the marginal contribution difficult. Ridge Regression (RR) is a popular alternative to consider in this scenario; however, doing so impairs the standard approach for statistical testing. The Raise Method (RM) is a technique that was developed to combat multicollinearity while maintaining statistical inference. In this work, we offer a novel approach for determining the raise parameter, because the traditional one is a function of actual coefficients, which limits the use of Raise Method in real-world circumstances. Using simulations, the suggested method was compared to Ordinary Least Squares and Ridge Regression in terms of its capacity to forecast, stability of its coefficients, and probability of obtain- ing unacceptable coefficients at different levels of sample size, linear dependence, and residual variance. According to the findings, the technique that we designed turns out to be quite effective. Finally, a practical application is discussed. Keywords Multicollinearity, OLS, Ridge Regression, Raise Regression, VIF 1 Introduction A typical linear regression model is y = Xβ + ε (1) where y denotes a n×1 vector of observations on the response variable, X is a n × p (n ≥ p) matrix of observations on the predictor variables, β is a p × 1 vector of unknown regression coefficients to be estimated and ε is a n × 1 vector of residual such that E(ε)=0 and E(εε T )= σ 2 I n , where I n denotes the identity matrix of order n. Then one can apply Ordinary Least Squares (OLS) method to estimate the unknown parameters, and the corresponding estimate is  β = ( X T X ) -1 X T y (2) And the corresponding variance of the estimator is V (  β) = ( X T X ) -1 σ 2 (3) It can be seen from equations (2) and (3) that when two or more predictor variables are perfectly linearly related, the estimation becomes impossible and the variance is indeterminate. Even if the interdependency is very high, which may not be perfect, un- desirable results will be obtained. This problem is called mul- ticollinearity. Ragnar Frisch was the one who coined the word ”multicollinearity” [1]. It is a serious threat to proper specifica- tion and the effective estimation of the structural relationship. As the relationship between variables increases, whether it is in the positive or negative direction, the standard error of the re- gression coefficients increases. i.e., even though the OLS pro- cedure gives unbiased estimates, they become unstable. Due to this, the confidence intervals become wider, test procedures lead to misleading results, unexpected signs in the coefficients,