A2023
Title: Large-scale linear hypothesis testing for high-dimensional renewable M-estimator
Authors: Myeonghun Yu - Ewha Womans University (Korea, South) [presenting]
Tate Jacobson - Oregon State University (United States)
Daeyoung Ham - The University of Texas at San Antonio (United States)
Abstract: Renewable estimation targets streaming-data settings where historical raw observations are unavailable or cannot be repeatedly processed. Existing renewable methods are computationally efficient, but batchwise approximation errors may accumulate and invalidate high-dimensional inference. A renewable inference framework is developed that is first-order insensitive to errors from previous estimators. The method uses only the current data batch and stored summary statistics, and introduces a surrogate loss that removes the leading accumulated approximation error. For linear hypothesis testing in high-dimensional sparse models, the surrogate loss is combined with partial penalization and local linear approximation algorithms for the full and reduced models. The computed LLA solutions coincide with the corresponding renewable oracle estimators with overwhelming probability. Using this strong oracle property and the asymptotic distribution of the renewable oracle estimators, the resulting partially penalized test statistic is asymptotically chi-square. The proposed framework yields implementable online tests without repeated access to historical raw data and applies to a broad class of models, with finite-sample performance supported by numerical experiments.
