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Confidence sets are of key importance in high-dimensional statistical inference. Under case–control study, a popular response-selective sampling design in medical study or econometrics, we consider the confidence intervals and statistical tests for single or low-dimensional parameters in high-dimensional logistic regression model. The asymptotic properties of the resulting estimators are established under mild conditions. We also study statistical tests for testing more general and complex hypotheses of the high-dimensional parameters. The general testing procedures are proved to be asymptotically exact and have satisfactory power. Numerical studies including extensive simulations and a real data example confirm that the proposed method performs well in practical settings.

Post-selection Inference of High-dimensional Logistic Regression Under Case–Control Design