Permutation tests in the two-sample problem for functional data

TL;DR

This paper compares three permutation test schemes for the two-sample problem in functional data, introducing new methods based on data depth and k-nearest-neighbors, and evaluates their performance through simulations and real data.

Contribution

It introduces two novel permutation test methods for functional data based on data depth and k-nearest-neighbors, and compares them with existing tests.

Findings

New methods show competitive power in simulations.

Depth-based methods provide robust significance assessments.

Computational costs vary among the methods.

Abstract

Three different permutation test schemes are discussed and compared in the context of the two-sample problem for functional data. One of the procedures was essentially introduced by Lopez-Pintado and Romo (2009), using notions of functional data depth to adapt the ideas originally proposed by Liu and Singh (1993) for multivariate data. Of the new methods introduced here, one is also based on functional data depths, but uses a different way (inspired by Meta-Analysis) to assess the significance of the depth differences. The second new method presented here adapts, to the functional data setting, the k-nearest-neighbors statistic of Schilling (1986). The three methods are compared among them and against the test of Horvath and Kokoszka (2012) in simulated examples and real data. The comparison considers the performance of the statistics in terms of statistical power and in terms of computational cost.