Oracle inequalities for sign constrained generalized linear models

High-dimensional data have recently been analyzed because of advancements in data collection technology. Although many methods have been developed for sparse recovery in the past 20 years, most of these methods require the selection of tuning parameters. This requirement means that the results obtained with these methods heavily depend on tuning. Theoretical properties are developed for sign-constrained generalized linear models with convex loss function, which is one of the sparse regression methods that does not require tuning parameters. Recent studies on this subject have shown that, in the case of linear regression, sign-constraints alone could be as efficient as the oracle method if the design matrix enjoys a suitable assumption in addition to a traditional compatibility condition. This type of result is generalized to a model that encompasses logistic and quantile regressions. Some numerical experiments are performed to confirm the theoretical findings.