Resampling-free inference for time series via RKHS embedding

2026-01-01

Electronic Journal of Statistics

AI Summary

This work proposes a nonparametric kernel-based approach for inference in multivariate or functional time series, addressing problems such as goodness-of-fit testing, change-point detection in marginal distributions, and independence testing. The method avoids both resampling and bandwidth selection by embedding the data into a reproducing kernel Hilbert space (RKHS) and constructing test statistics through sample splitting, projection, and self-normalization. Leveraging a novel conditioning technique, the authors establish that the resulting test statistic admits a pivotal asymptotic null distribution under strong mixing conditions and analyze its power against local alternatives. The proposed procedure achieves high finite-sample accuracy while substantially improving computational efficiency, outperforming existing resampling-based methods.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of two time series, among others. Most methodologies available in the existing literature address these problems by employing a bandwidth-dependent bootstrap or subsampling approach, which can be computationally expensive and/or sensitive to the choice of bandwidth. To address these limitations, we propose a novel class of kernel-based tests by embedding the data into a reproducing kernel Hilbert space, and construct test statistics using sample splitting, projection, and self-normalization (SN) techniques. Through a new conditioning technique, we demonstrate that our test statistics have pivotal limiting null distributions under strong mixing and mild moment assumptions. We also analyze the limiting power of our tests under local alternatives. Finally, we showcase the superior size accuracy and computational efficiency of our methods as compared to some existing ones.

Problem

• nonparametric inference
• time series
• resampling
• goodness-of-fit
• change point

Innovation

• RKHS embedding
• resampling-free inference
• self-normalization
• kernel-based test
• time series