For modeling count data, the Poisson regression model is widely used in which response variable takes non-negative integer values. However, presence of strong correlation between explanatory variables causes problem multicollinearity. Due to multicollinearity, variance maximum likelihood estimator (MLE) will be inflated causing parameters estimation become unstable. Multicollinearity can tackle...

Identifying influential observations is an important part of the model building process in linear regression. There are numerous diagnostic measures based on different approaches regression analysis. However, problem multicollinearity and may occur simultaneously. Therefore, we propose new two parameter ridge estimator defined by Lipovetsky Conklin (2005) alternative to usual ordinary We define...

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...

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing MSE (mean square error) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collin...

In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of ridge regression for prediction in quantitative genetics using single-nucleotide polymorphism data is discussed. In parti...