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This paper analyzes the possibilities of using the generalized ridge regression to mitigate multicollinearity in a multiple linear regression model. For this purpose, we obtain the expressions for the estimated variance, the coefficient of…
This paper shows that the degree of approximate multicollinearity in a linear regression model increases simply by including independent variables, even if these are not highly linearly related. In the current situation where it is…
When the regressors of a econometric linear model are nonorthogonal, it is well known that their estimation by ordinary least squares can present various problems that discourage the use of this model. The ridge regression is the most…
While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…
Ridge estimator is an alternative to ordinary least square estimator when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose new estimators which are modifications of the…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Weighting procedures are used in observational causal inference to adjust for covariate imbalance within the sample. Common practice for inference is to estimate robust standard errors from a weighted regression of outcome on treatment.…
The literature shows the possible existence of a problem called collinearity in both Nelson-Siegel and Nelson-Siegel-Svensson models due to the relationship between the slope and curvature components. The presence of this problem and the…
High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by…
This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…
Multicollinearity is relevant to many different fields where linear regression models are applied, and its existence may affect the analysis of ordinary least squares (OLS) estimators from both the numerical and statistical points of views.…
In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression…
Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the…
Background: Multicollinearity inflates the variance of OLS coefficients, widening confidence intervals and reducing inferential reliability. Yet fixed variance inflation factor (VIF) cut-offs are often applied uniformly across studies with…
We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also,…
Beta regression model is useful in the analysis of bounded continuous outcomes such as proportions. It is well known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood…
Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…