# Lasso Regression as Variable Selection

Suppose we are initially given $$p$$ predictor variables. In lasso regression, we want to find estimates of the coefficients $$\beta_1, \dots, \beta_p$$ that minimize $$\text{RSS}+ \lambda \sum_{j=1}^{p} |\beta_j|$$ where $$\text{RSS}$$ is the residual sum of squares. So if $$\lambda = 0$$ then we just have regular ordinary least squares regression. As we increase $$\lambda$$, we are essentially assuming more structure in the data and so increase the bias and reduce the variance compared to OLS. Basically we are assuming a prior distribution for the coefficients. Now some of the coefficients can be $$0$$. So this is also a variable selection procedure.

Question. Can one first do a lasso regression and then some sort of stepwise selection technique for variable reduction? Does the order of performing these techniques matter?