A0415
Title: Testing of regression coefficients under over-parameterized model with hidden confounders
Authors: Yeheng Ge - The Hong Kong Polytechnic University (China) [presenting]
Xingdong Feng - Shanghai University of Finance and Economics (China)
Mengyun Wu - Shanghai University of Finance and Economics (China)
Shuyan Chen - University of Science and Technonogy of China (China)
Tao Li - Shanghai University of Finance and Economics (China)
Abstract: The existing high-dimensional inference methods could be invalid due to the existence of hidden confounders and non-sparse control variables. A novel parameter inference method is proposed based on the ridge estimator for the over-parameterized model, which is consistent and asymptotically normal even as the non-sparse high dimensional control variables and hidden confounders are present. The proposed method has a closed-form solution, which is new in high dimensional inference and hence can be easily applied to the inference for streaming data. The convergence rate of the bias and variance term is established under various data-generating schemes. A phase transition phenomenon is observed under the cases of $n<p$ and $n>p$, and the corresponding asymptotic results are established. The finite sample performance of the proposed method is well illustrated with simulation studies and real data applications on the GTEx project and FRED-QD database.
