  High-dimensional data have recently been analyzed because of data collection
technology evolution. Although many methods have been developed to gain sparse
recovery in the past two decades, most of these methods require selection of
tuning parameters. As a consequence of this feature, results obtained with
these methods heavily depend on the tuning. In this paper we study the
theoretical properties of sign-constrained generalized linear models with
convex loss function, which is one of the sparse regression methods without
tuning parameters. Recent studies on this topic have shown that, in the case of
linear regression, sign-constrains alone could be as efficient as the oracle
method if the design matrix enjoys a suitable assumption in addition to a
traditional compatibility condition. We generalize this kind of result to a
much more general model which encompasses the logistic and quantile
regressions. We also perform some numerical experiments to confirm theoretical
findings obtained in this paper.
