Generalized Ridge Regression Estimator in High Dimensional Sparse Regression Models
AbstractModern statistical analysis often encounters linear models with the number of explanatory variables much larger than the sample size. Estimation in these high-dimensional problems needs some regularization methods to be employed due to rank deficiency of the design matrix. In this paper, the ridge estimators are considered and their restricted regression counterparts are proposed when the errors are dependent under a multicollinearity and high-dimensionality setting. The asymptotic distributions of the proposed estimators are exactly derived. Incorporating the information contained in the restricted estimator, a shrinkage type ridge estimator is also exhibited and its asymptotic risk is analyzed under some special cases. To evaluate the efficiency of the proposed estimators, a Monte-Carlo simulation along with a real example are considered.
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