General model-free weighted envelope estimation

Envelope methodology is succinctly pitched as a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives [5, first sentence page 1]. This description comes with the additional caveat that gains obtained by envelope are mitigated model selection volatility to an unknown degree. Recent strides account have been made on two fronts: 1) development weighted estimator this variability directly context linear regression model; 2) criteria facilitate consistent dimension more general settings. We unify these directions and provide estimators associated appropriate estimation Our technique provides practitioners robust useful variance reduction finite samples. Theoretical empirical justification given our validity nonparametric bootstrap procedure estimating their asymptotic established. Simulation studies real data analysis support claims demonstrate advantage when present.