  Model selection (MS) and model averaging (MA) are two popular approaches when
having many candidate models. Theoretically, the estimation risk of an oracle
MA is not larger than that of an oracle MS because the former one is more
flexible, but a foundational issue is: does MA offer a {\it substantial}
improvement over MS? Recently, a seminal work: Peng and Yang (2021), has
answered this question under nested models with linear orthonormal series
expansion. In the current paper, we further reply this question under linear
nested regression models. Especially, a more general nested framework,
heteroscedastic and autocorrelated random errors, and sparse coefficients are
allowed in the current paper, which is more common in practice. In addition, we
further compare MAs with different weight sets. Simulation studies support the
theoretical findings in a variety of settings.
