Statistics practitioners have been depending on the ordinary least squares (OLS) method in linear regression model for generation because of its optimal properties and simplicity calculation. However, OLS estimators can be strongly affected by existence multicollinearity which is a near dependency between two or more independent variables model. Even though presence estimate still remained unbi...

Modified (r, k) class ridge regression (MCRR) which includes unbiased ridge regression (URR), (r, k) class, principal components regression (PCR) and the ordinary least squares (OLS) estimators is proposed in regression analysis, to overcome the problem of multicollinearity. In this paper, we derive the necessary and sufficient conditions for the superiority of the MCRR estimator over each of t...

In multiple regression analysis, the independent variables should be uncorrelated within each other. If they are highly intercorrelated, this serious problem is called multicollinearity. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. In this paper, we will propose some modified ridge parameters. We will compare our estimators with so...

Documenting the process of consumer attitude formation toward brand extensions has proved elusive, with variations in results between Aaker & Keller’s original study and subsequent replications. This study moves beyond the student sample and adjusts for multicollinearity, providing a robust empirical foundation for generalising components of the original model. It provides general support for t...

We propose a new estimator to combat the multicollinearity in the linear model when there are stochastic linear restrictions on the regression coefficients. The new estimator is constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator, which is called the stochastic restricted principal components (SRPC) regression estimator. Necessary ...

Statistical literature has several methods for coping with multicollinearity. This paper introduces a new shrinkage estimator, called modified unbiased ridge (MUR). This estimator is obtained from unbiased ridge regression (URR) in the same way that ordinary ridge regression (ORR) is obtained from ordinary least squares (OLS). Properties of MUR are derived. Results on its matrix mean squared er...

In this paper offers a simple and lossless compression method for compression of medical images. Method is based on wavelet decomposition of the medical images followed by the correlation analysis of coefficients. The correlation analyses are the basis of prediction equation for each sub band. Predictor variable selection is performed through coefficient graphic method to avoid multicollinearit...

We introduce a new regression method – called Correlated Component Regression (CCR) – which provides reliable predictions even with near multicollinear data. Near multicollinearity occurs when a large number of correlated predictors and relatively small sample size exists as well as situations involving a relatively small number of correlated predictors. Different variants of CCR are tailored t...

Consider the linear regression model y = X + u in the usual notation. In many applications the design matrix X is frequently subject to severe multicollinearity. In this paper an alternative estimation methodology, maximum entropy is given and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We described the generalized maximum entropy (GME) ...