Speaker
Description
Testing independence between functional observations remains a fundamental challenge in modern statistics, particularly in settings involving high-dimensional or infinite-dimensional random objects. The presented work introduces a new framework for independence testing in functional data based on the distance of mean embedding (DIME), a metric recently proposed as a flexible alternative to classical kernel-based measures such as the Hilbert–Schmidt independence criterion (HSIC).
The methodology consists of two main steps. First, functional observations (univariate or multivariate) are represented through basis expansion, reducing infinite-dimensional functions to finite-dimensional coefficient vectors. Second, independence is assessed using DIME, which offers greater flexibility than HSIC by allowing freedom in the choice of characteristic kernels and of the embedding measure.
The procedure further incorporates marginal aggregation to improve performance in pairwise independence testing and extends naturally to mutual independence through symmetric and asymmetric aggregation schemes. Simulation studies demonstrate that the proposed tests maintain nominal type I error rates and often achieve higher power than methods based on distance covariance or HSIC.
The new independence testing procedures were applied to two real-world examples: air pollution and chemometric sugar spectra data. For the U.S. air pollution data, the methods were employed to verify pairwise and mutual independence among various pollutants (NO2, O3, SO2, and CO). Significant dependence between the air pollutants was detected. In the chemometric sugar spectra data, the independence tests were utilized to check the independence between a group of three excitation wavelengths, previously found useful for predicting ash content, and the remaining four wavelengths. The tests confirmed strong dependence between these two sets of functional variables. This indecates the correctness of the proposed functional regression model and that not all excitation wavelengths have to be used in the analysis.
Overall, the DIME-based framework provides a robust and powerful alternative for independence testing in functional data analysis.
32144107608