Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation

Monday, September 16, 2019 - 2:30pm - 3:30pm
Lind 305
Runze Li (The Pennsylvania State University)
We develop a new estimation and valid inference method for low-dimensional regression coefficients in high-dimensional generalized linear models. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the selected variables. The proposed confidence interval (CI) achieves valid coverage without assuming consistency of the model selection
procedure. When the selection consistency is achieved, we show the length of the proposed CI is asymptotically the same as the CI of the oracle method which works as well as if the support of the control variables were known. In addition, we prove the proposed CI is asymptotically narrower than the CIs constructed based on the de-sparsified Lasso estimator and the decorrelated score statistic. Simulation studies and real data applications are presented to back up our theoretical findings.