Abstract
For high dimensional linear model with error-in-variables, a novel debiased procedure is developed and analyzed to construct component-wise confidence intervals of the regression coefficient. The proposed method is not only able to account for measurement errors to avoid non-vanishing biases, but also to compensate the biases introduced by penalization. The resulting estimator is asymptotically unbiased and normal under mild conditions. Then it can be used to construct valid confidence intervals and conduct hypothesis tests. Results of an extensive simulation study are also presented to show the efficacy and usefulness of our procedure.
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