Statistical inference for the low dimensional parameters of linear regression models in the presence of high-dimensional data: An orthogonal projection approach

We consider the estimation and statistical inference for low dimensional parameters for a regression model with covariates whose dimension increases with sample size. We suggest a computationally simple one stage orthogonal projection approach to estimate the low dimensional parameters under strict or approximate sparsity conditions. The orthogonal projection approach is simple to implement and the inference for the low dimensional parameters is straightforward to derive whether the high dimensional function is linear or nonlinear. It also avoids the complicated regularization bias issues commonly associated with two stage estimation methods. Monte Carlo simulations and empirical applications are also conducted to investigate the finite sample performance of the proposed estimator vs the double/debiased estimator of Belloni et al. (2014) and Chernozhukov et al. (2018).