Bootstrapped Edge Count Tests for Nonparametric Two-Sample Inference Under Heterogeneity
Nonparametric two-sample testing is a classical problem in inferential statistics. While modern two-sample tests, such as the edge count test and its variants, can handle multivariate and non-Euclidean data, contemporary gargantuan datasets often exhibit heterogeneity due to the presence of latent subpopulations. Direct application of these tests, without regulating for such heterogeneity, may lead to incorrect statistical decisions. We develop a new nonparametric testing procedure that accurately detects differences between the two samples in the presence of unknown heterogeneity in the data generation process. Our framework handles this latent heterogeneity through a composite null that entertains the possibility that the two samples arise from a mixture distribution with identical component distributions but with possibly different mixing weights. In this regime, we study the asymptotic behavior of weighted edge count test statistic and show that it can be effectively re-calibrated to detect arbitrary deviations from the composite null. For practical implementation we propose a Bootstrapped Weighted Edge Count test which involves a bootstrap-based calibration procedure that can be easily implemented across a wide range of heterogeneous regimes. A comprehensive simulation study and an application to detecting aberrant user behaviors in online games demonstrates the excellent non-asymptotic performance of the proposed test.
Code (0)
등록된 구현이 없습니다.
Tasks
Two-sample testingVocal Bursts Valence PredictionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Efficient Aggregated Kernel Tests using Incomplete $U$-statistics
We propose a series of computationally efficient nonparametric tests for the two-sample, independence, and goodness-of-fit problems, using the Maximum Mean Discrepancy (MMD), Hilbert Schmidt Independence Criterion (HSIC)…
Computational EfficiencyPermutation Tests at Nonparametric Rates
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper propos…
Fisher-Pitman permutation tests based on nonparametric Poisson mixtures with application to single cell genomics
This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood …
Robust Inference on Infinite and Growing Dimensional Time Series Regression
We develop a class of tests for time series models such as multiple regression with growing dimension, infinite-order autoregression and nonparametric sieve regression. Examples include the Chow test and general linear r…
regressionTime SeriesTime Series AnalysisTime Series RegressionEncompassing Tests for Nonparametric Regressions
We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testi…
regression