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We consider random sample splitting for estimation and inference in highdimensional generalized linear models, where we first apply the lasso to selecta submodel using one subsample and then apply the debiased lasso to fit theselected model using the remaining subsample. We show that, no matter includinga prespecified subset of regression coefficients or not, the debiased lassoestimation of the selected submodel after a single splitting follows a normaldistribution asymptotically. Furthermore, for a set of prespecified regressioncoefficients, we show that a multiple splitting procedure based on the debiasedlasso can address the loss of efficiency associated with sample splitting andproduce asymptotically normal estimates under mild conditions. Our simulationresults indicate that using the debiased lasso instead of the standard maximumlikelihood estimator in the estimation stage can vastly reduce the bias andvariance of the resulting estimates. We illustrate the proposed multiplesplitting debiased lasso method with an analysis of the smoking data of theMid-South Tobacco Case-Control Study.

Debiased Lasso After Sample Splitting for Estimation and Inference in High Dimensional Generalized Linear Models