  For linear regression models who are not exactly sparse in the sense that the
coefficients of the insignificant variables are not exactly zero, the working
models obtained by a variable selection are often biased. Even in sparse cases,
after a variable selection, when some significant variables are missing, the
working models are biased as well. Thus, under such situations, root-n
consistent estimation and accurate prediction could not be expected. In this
paper, a novel remodelling method is proposed to produce an unbiased model when
quasi-instrumental variables are introduced. The root-n estimation consistency
and the asymptotic normality can be achieved, and the prediction accuracy can
be promoted as well. The performance of the new method is examined through
simulation studies.
