2011/09/12 by SM Enayetur Raheem, Raheem, SM Enayetur, S. Ejaz Ahmed +1
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Optimal Experimental Design Methods #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1109.2527
openalex publication_date 2011/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a problem of predicting a response variable using a set of\ncovariates in a linear regression model. If it is \a priori known or\nsuspected that a subset of the covariates do not significantly contribute to\nthe overall fit of the model, a restricted model that excludes these\ncovariates, may be sufficient. If, on the other hand, the subset provides\nuseful information, shrinkage method combines restricted and unrestricted\nestimators to obtain the parameter estimates. Such an estimator outperforms the\nclassical maximum likelihood estimators. Any \prior information may be\nvalidated through preliminary test (or pretest), and depending on the validity,\nmay be incorporated in the model as a parametric restriction. Thus, pretest\nestimator chooses between the restricted and unrestricted estimators depending\non the outcome of the preliminary test. Examples using three real life data\nsets are provided to illustrate the application of shrinkage and pretest\nestimation. Performance of positive-shrinkage and pretest estimators are\ncompared with unrestricted estimator under varying degree of uncertainty of the\nprior information. Monte Carlo study reconfirms the asymptotic properties of\nthe estimators available in the literature.\n