  Consider a problem of predicting a response variable using a set of
covariates in a linear regression model. If it is \emph{a priori} known or
suspected that a subset of the covariates do not significantly contribute to
the overall fit of the model, a restricted model that excludes these
covariates, may be sufficient. If, on the other hand, the subset provides
useful information, shrinkage method combines restricted and unrestricted
estimators to obtain the parameter estimates. Such an estimator outperforms the
classical maximum likelihood estimators. Any \emph{prior} information may be
validated through preliminary test (or pretest), and depending on the validity,
may be incorporated in the model as a parametric restriction. Thus, pretest
estimator chooses between the restricted and unrestricted estimators depending
on the outcome of the preliminary test. Examples using three real life data
sets are provided to illustrate the application of shrinkage and pretest
estimation. Performance of positive-shrinkage and pretest estimators are
compared with unrestricted estimator under varying degree of uncertainty of the
prior information. Monte Carlo study reconfirms the asymptotic properties of
the estimators available in the literature.
