The detection of influential observations has attracted a great deal of attention in last few decades. Most of the ideas of determining influential observations are based on single-case diagnostics with ith case deleted. The Cook’s distance are most commonly used among the other single-case diagnostics and successfully applied to various statistical models. In this article, we propose Cook’s di...

Abstract: Identifying influential observations is an important part of the model building process in linear regression. There are numerous diagnostic measures based on different approaches in linear regression analysis. However, the problem of multicollinearity and influential observations may occur simultaneously. Therefore, we propose new diagnostic measures based on the two parameter ridge e...

Ridge regression is one of the most popular and effective regularized regression methods, and one case of particular interest is that the number of features p is much larger than the number of samples n, i.e. p n. In this case, the standard optimization algorithm for ridge regression computes the optimal solution x⇤ in O(n2p + n3) time. In this paper, we propose a fast relativeerror approximati...

Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into accoun...

Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into accoun...

Topics in Reduced Rank methods for Multivariate Regression by Ashin Mukherjee Advisors: Professor Ji Zhu and Professor Naisyin Wang Multivariate regression problems are a simple generalization of the univariate regression problem to the situation where we want to predict q(> 1) responses that depend on the same set of features or predictors. Problems of this type is encountered commonly in many...

This paper presents a new methodology for regularizing data-based predictive models. Traditional modeling using regression can produce unrepeatable, unstable, or noisy predictions when the inputs are highly correlated. Ridge regression is a regularization technique used to deal with those problems. A drawback of ridge regression is that it optimizes a single regularization parameter while the m...