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arXiv

Without knowing the covariate distribution, a new stochastic-approximation estimator attains parametric rates in logistic regression with missing covariates and provably beats complete-case analysis

For logistic regression with an unknown (but bounded) covariate distribution and coordinate-wise missing-completely-at-random covariates, the authors construct a distribution-free estimating equation from a monotone operator and solve it with a projected stochastic approximation algorithm; they prove parametric-rate signal recovery with risk characterized by the missingness profile, show the estimator is never worse than the complete-case estimator, and provide a matching minimax lower bound under homogeneous missingness showing the nonstandard dependence on the observation probability is intrinsic.