  To successfully work on variable selection, sparse model structure has become
a basic assumption for all existing methods. However, this assumption is
questionable as it is hard to hold in most of cases and none of existing
methods may provide consistent estimation and accurate model prediction in
nons-parse scenarios. In this paper, we propose semiparametric re-modeling and
inference when the linear regression model under study is possibly non-sparse.
After an initial working model is selected by a method such as the Dantzig
selector adopted in this paper, we re-construct a globally unbiased
semiparametric model by use of suitable instrumental variables and
nonparametric adjustment. The newly defined model is identifiable, and the
estimator of parameter vector is asymptotically normal. The consistency,
together with the re-built model, promotes model prediction. This method
naturally works when the model is indeed sparse and thus is of robustness
against non-sparseness in certain sense. Simulation studies show that the new
approach has, particularly when $p$ is much larger than $n$, significant
improvement of estimation and prediction accuracies over the Gaussian Dantzig
selector and other classical methods. Even when the model under study is
sparse, our method is also comparable to the existing methods designed for
sparse models.
