- (2014) based on the simulation setting of the main text. We use cross-validation to choose the regularization parameters as this is the most commonly-used method in this literature.
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- B Debiased Lasso In this section, we present theoretical and simulation results on the OVB of the debiased Lasso proposed by van de Geer et al. (2014). B.1 Theoretical results The idea of debiased Lasso is to start with an initial Lasso estimate Î¸Ì = αÌ, Î²Ì of θâ = (αâ , βâ ) in equation (1), where αÌ, Î²Ì â arg min αâR,βâRp 1 2n |Y â Dα â Xβ|2 2 + λ1 (|α| + |β|1) . (45) Given the initial Lasso estimator αÌ, the debiased Lasso adds a correction term to Î±Ì to reduce the bias introduced by regularization. In particular, the debiased Lasso takes the form Î±Ì = Î±Ì + â¦Ì1 n n X i=1 ZT i Yi â ZiÎ¸Ì , (46) where Zi = (Di, Xi) and â¦Ì1 is the first row of â¦Ì, which is an approximate inverse of 1 n
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