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Kernel Tests for One, Two, and K-Sample Goodness-of-Fit: State of the Art and Implementation Considerations

  • Yang Chen
  • Marianthi MarkatouEmail author
Chapter
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Part of the Emerging Topics in Statistics and Biostatistics book series (ETSB)

Abstract

In this article, we first discuss the fundamental role of statistical distances in the problem of goodness-of-fit and review various existing multivariate two-sample goodness-of-fit tests from both statistics and machine learning literature. The review conducted delivers the fact that there does not exist a satisfactory multivariate two-sample goodness-of-fit test. We introduce a class of one and two-sample tests constructed using the kernel-based quadratic distance, and briefly touch upon their asymptotic properties. We discuss the practical implementation of these tests, with emphasis on the kernel-based two-sample test. Finally, we use simulations and real data to illustrate the application of the kernel-based two-sample test, and compare this test with tests existing in the literature.

Keywords

Goodness-of-fit Kernel tests Quadratic distance Multivariate Two-sample methods 

Notes

Acknowledgement

The work of both authors is supported by The Troup Fund of the Kaleida Health Foundation.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity at BuffaloBuffaloUSA

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