Authors

• SM Enayetur Raheem
• S. Ejaz Ahmed

Abstract

Consider a problem of predicting a response variable using
a set of covariates in a linear regression model. If it is 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 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.

Keywords

• Data Analysis
• James-Stein estimation
• LASSO
• Monte Carlo Simulation
• Multiple regression
• pretest estimation
• quadratic risk
• RMSE
• shrinkage estimation