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Two extensions of generalized linear models are considered. In the first one,response variables depend on multiple linear combinations of covariates. In thesecond one, only response variables are observed while the linear covariatesare missing. We derive stochastic Lipschitz continuity results for the lossfunctions involved in the regression problems and apply them to get bounds onestimation error for Lasso. Multivariate comparison results on Rademachercomplexity are obtained as tools to establish the stochastic Lipschitzcontinuity results.

Stochastic Lipschitz continuity for high dimensional Lasso with multiple linear covariate structures or hidden linear covariates