Nonparametric Testing under Random Projection
This addresses computational bottlenecks in nonparametric testing for researchers and practitioners dealing with large datasets, though it appears incremental as it builds on existing kernel ridge regression frameworks.
The paper tackles the high computational complexity of nonparametric inference with large data by developing an efficient testing method using random projections in kernel ridge regression, achieving testing optimality with a derived minimum number of projections and establishing an adaptive procedure without prior regularity knowledge.
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the specific kernel ridge regression setup, a simple distance-based test statistic is proposed. Notably, we derive the minimum number of random projections that is sufficient for achieving testing optimality in terms of the minimax rate. An adaptive testing procedure is further established without prior knowledge of regularity. One technical contribution is to establish upper bounds for a range of tail sums of empirical kernel eigenvalues. Simulations and real data analysis are conducted to support our theory.