A new graph-based two-sample test for multivariate and object data

Abstract

Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can be applied to multivariate data and non-Euclidean data as long as a dissimilarity measure on the sample space can be defined, which can usually be provided by domain experts. Existing tests based on a similarity graph lack power either for location or for scale alternatives. The new test utilizes a common pattern that was overlooked previously, and works for both types of alternatives. The test exhibits substantial power gains in simulation studies. Its asymptotic permutation null distribution is derived and shown to work well under finite samples, facilitating its application to large data sets. The new test is illustrated on two applications: The assessment of covariate balance in a matched observational study, and the comparison of network data under different conditions.

References in corpus (1)

• Covariate Balance in Simple, Stratified and Clustered Comparative Studies

Cited by in corpus (34)

• A weighted edge-count two-sample test for multivariate and object data
• Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation
• Sequential Change-point Detection for High-dimensional and non-Euclidean Data
• Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders
• Generalized Kernel Two-Sample Tests
• Methods for Quantifying Dataset Similarity: a Review, Taxonomy and Comparison
• On high-dimensional modifications of some graph-based two-sample tests
• Robust Multivariate Nonparametric Tests via Projection-Averaging
• An Efficient and Distribution-Free Two-Sample Test Based on Energy Statistics and Random Projections
• Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes
• Nonparametric data segmentation in multivariate time series via joint characteristic functions
• Asymptotic Distribution-Free Change-Point Detection for Multivariate and non-Euclidean Data
• Distribution-Free Multisample Test Based on Optimal Matching with Applications to Single Cell Genomics
• Limiting distributions of graph-based test statistics on sparse and dense graphs
• Bayesian graphical compositional regression for microbiome data
• A Normality Test for High-dimensional Data based on a Nearest Neighbor Approach
• These Unprecedented Times: The Dynamic Pattern Of COVID-19 Deaths Around The World
• New multivariate tests for assessing covariate balance in matched observational studies
• Online Graph-Based Change-Point Detection for High Dimensional Data
• Hypothesis Testing for Two Sample Comparison of Network Data
• Weighted-Graph-Based Change Point Detection
• Graph-based multiple change-point detection
• Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data
• Asymptotic Distribution and Detection Thresholds for Two-Sample Tests Based on Geometric Graphs
• 3D Shape Generation with Grid-based Implicit Functions
• Two edge-count tests and relevance analysis in k high-dimensional samples
• Two-sample tests for repeated measurements of histogram objects with applications to wearable device data
• Asymptotic Distribution-free Change-point Detection for Modern Data Based on a New Ranking Scheme
• The AUGUST Two-Sample Test: Powerful, Interpretable, and Fast
• A label-efficient two-sample test
• A fast and effective kernel two-sample test for large-scale data
• A new non-parametric test for multivariate paired data from pair matching or paired designs
• A Goodness-of-Fit Test for Statistical Models
• A note on the permutation distribution of generalized correlation coefficients