  This article is concerned with the Bridge Regression, which is a special
family in penalized regression with penalty function
$\sum_{j=1}^{p}|\beta_j|^q$ with $q>0$, in a linear model with linear
restrictions. The proposed restricted bridge (RBRIDGE) estimator simultaneously
estimates parameters and selects important variables when a prior information
about parameters are available in either low dimensional or high dimensional
case. Using local quadratic approximation, the penalty term can be approximated
around a local initial values vector and the RBRIDGE estimator enjoys a
closed-form expression which can be solved when $q>0$. Special cases of our
proposal are the restricted LASSO ($q=1$), restricted RIDGE ($q=2$), and
restricted Elastic Net ($1< q < 2$) estimators. We provide some theoretical
properties of the RBRIDGE estimator under for the low dimensional case, whereas
the computational aspects are given for both low and high dimensional cases. An
extensive Monte Carlo simulation study is conducted based on different prior
pieces of information and the performance of the RBRIDGE estiamtor is compared
with some competitive penalty estimators as well as the ORACLE. We also
consider four real data examples analysis for comparison sake. The numerical
results show that the suggested RBRIDGE estimator outperforms outstandingly
when the prior is true or near exact
